A constructivist, active-learning curriculum for high school physics

Contact(s):

Leonard, William J. MOP is a one-year curriculum for high school physics. It is the result of a materials development project supported by the National Science Foundation, and its design was guided by educational research findings. The curriculum integrates topics traditionally taught at different times of the year, and students are expected to develop conceptual understanding of physics while improving problem-solving proficiency.

A description of the intent and nature of the Minds-On Physics curriculum

During the past two decades, study after study has pointed out the shortcomings of high school physics courses: (a) The vast majority of students who take high school physics emerge with only a shallow understanding of miscellaneous facts and formulas; (b) What knowledge students do acquire is usually plagued with misconceptions, many of which persist despite instruction; and (c) With rare exception, students are unable to apply what they learn to explain, or to reason about, the world around them or to solve interesting, nontrivial problems. These unintended outcomes of physics instruction are the result of a mismatch between the way physics is typically taught and the way students go about the business of learning physics.

The **Minds•On Physics** (MOP) curriculum materials were specifically written to address this situation. In developing MOP, we have endeavored to take account of research on the teaching and learning of physics, which has grown steadily during the past twenty years. This research has brought to light many of the cognitive difficulties students face in trying to learn physics (see *Supplement B* in the *Teacher's Guide to accompany MOP: Motion*). It has also demonstrated the value of an active learning environment and cooperative group work for improving student learning and maintaining student interest (see *Supplements A and B* in the Motion Teacher's Guide). MOP is designed to be consonant with findings from many different strands of educational and cognitive research - prior conceptions, expert vs. novice differences, the cognitive load associated with different styles of questions, problem solving vs. conceptual understanding, active learning, cooperative group learning, and the effects of meta-communication on the learning process. We believe that MOP will provide teachers with an approach to physics instruction that is better matched to the learning needs of students, and thereby improve the quality of the educational experience for both students and teachers.

MOP is an activity-based, full-year curriculum for high school physics. It is intended to be an excellent preparation for college-level science, and is well matched with the National Research Council's National Science Education Standards. (See *Supplement C* in the Motion Teacher's Guide for a comparison with the 1996 standards.) The MOP activities were designed to help students learn to use physics concepts to analyze and solve problems, and to curb students' natural tendency to learn by rote and to engage in formula manipulation. Most of the activities are well suited for use in cooperative group settings. Through careful construction and sequencing, MOP activities encourage students (a) to explore their existing understanding of physics-like concepts, (b) to refine their understanding of formal physics concepts and to investigate connections among related concepts, (c) to use physics concepts and principles to analyze and reason about physical situations without recourse to equation pushing, (d) to develop problem-solving skills that are anchored in an understanding of fundamental concepts and principles, and (e) to put together seemingly isolated pieces of physics knowledge into a unified, meaningful whole. Our goal is to enable students to obtain a deeper understanding of physics concepts and a greater facility for applying them to novel situations - or at the very least to point them in the right direction.

Although the MOP activities place a premium on conceptual development, the MOP curriculum should not be viewed as a traditional conceptual-physics curriculum. Many MOP activities require a fairly high level of analytical reasoning and mathematical skill, more comparable to traditional problem-solving physics courses than to conceptual-physics courses. Similarly, MOP engages students in conceptual reasoning at a much deeper level than is typically the case in a conceptual-physics course - for that matter in any type of high school physics course. MOP is a challenging and rigorous course!

Nevertheless MOP is flexible enough to be used with a wide range of students. For example, MOP activities have been used in 8th and 9th grade physical science courses, and they have been used in graduate-level teacher preparation courses. This is possible because of the way MOP activities are sequenced. Initial activities focus on the students' understanding of concepts. Later activities help students build and refine a scientific understanding of physics concepts. Only then are students asked to do the more challenging activities that require complex analysis and reasoning skills. The quantitative/mathematical development of a topic only occurs after students have had sufficient opportunity to develop a thorough conceptual understanding. We believe that MOP can provide all students with the skills needed to succeed in physics, and that the materials help create a classroom environment that is active and inclusive.

Another reason many different levels and types of classes can use MOP is that the depth of coverage is determined by the teacher and the students, not the activity. This is the beauty of having questions at the core of the curriculum. Students at different stages of development will necessarily interpret them differently, and their answers will always reveal the depth and breadth of their understanding. And teachers can probe as much or as little as they desire into their students' thought processes.

Activities are the heart and soul of the MOP curriculum materials, but the MOP program is more than a set of student activities and associated materials. It is an approach to learning physics. Underlying the approach is a set of four basic principles:

- Knowledge is constructed by each learner, not transmitted to him or her by someone else.
- The construction of knowledge is an effortful process requiring significant time and engagement by the learner.
- The construction of knowledge often takes place within the context of social interaction.
- The construction of knowledge is greatly influenced by the knowledge the learner already possesses.

In recognition of these principles, MOP advocates an ** action-oriented** approach to learning physics. This means that MOP encourages little (if any) lecturing by the teacher, and requires minimal reading by the student prior to working on an activity. Instead, after a brief introduction to a new topic, students are quickly engaged in activities that require them to interact with other students and the teacher. Working in groups students use concepts to analyze problem situations and answer open-ended questions, explore the meaning of concepts through inquiry and hands-on activities, and share personal reflections on prior experiences. The approach treats students as sentient individuals, each one having a unique way of looking at a situation or solving a problem. The MOP approach builds on what students know, and it emphasizes processes, such as analyzing, reasoning, explaining and strategizing, over coverage of "physics facts."

**Content of MOP.** The MOP materials are contained in six volumes of student activities and six corresponding Teacher's Guides. The first three volumes of activities are the core of the MOP curriculum and can be covered in 1/2 to 3/4 of the school year. The first volume contains activities covering *Motion*. The second volume is on *Interactions*. The third treats *Conservation Laws & Concept-Based Problem Solving*. Taken together, we refer to these three volumes as *mechanics.*

The remaining three volumes constitute *supplemental* activities, which can be done for the final 1/4 to 1/2 of the school year. They are *Fundamental Forces & Fields*, *Complex Systems*, and *Advanced Topics in Mechanics*. The goal of each is to show how the concepts in mechanics can be applied to many other topics.

The materials require very little specialized or sophisticated equipment. In mechanics, most of the manipulatives that might be needed are common household items, such as balls, string, washers, marbles, and bathroom scales. However, it is helpful if teachers have access to basic equipment, such as dynamics carts, air tracks, and spring scales. Within the supplemental activities, some of the equipment needed is a little more specialized, but it should still be simple and familiar, such as batteries, magnets, wire, and nails.

**Assessment.** Traditional ways of testing students do little to uncover conceptual difficulties or to measure understanding of physical laws and principles. New ways of assessing students' progress must necessarily be developed alongside new approaches to teaching physics. New assessments need to encourage students to focus on those features that are important for deep understanding. In the *Instructional Aids for Teachers*, we provide a wealth of examples showing how to probe students' conceptual understanding and measure their progress with the new approach.

**Role of Teachers.** The MOP approach requires a different role for teachers. No longer are teachers dispensers of information. A teacher who uses the MOP approach spends less time preparing lectures and more time structuring experiences for students. Many activity questions actually have two or more justifiable answers, each of which depends on the assumptions made by the students answering the questions. Thus, emphasis should be shifted from answers and whether they are right or wrong, and placed on intelligent discussion of the questions and whether the answers are consistent with the assumptions and reasoning used. In this mode, a teacher serves as a facilitator, counselor, or coach, rather than a lecturer, turning students' attention toward those ideas that will eventually help them reach a satisfactory conclusion.

**Materials and Support for Teachers.** We have worked with teachers for many years. We are well aware of the difficulties teachers face in adopting a new curriculum, particularly if it is radically different from what they have used in the past. Realistically, it could take a teacher two to three years to become completely familiar with the MOP curriculum, and to make it their own. We have included with the MOP curriculum considerable support materials to make the transition easier and more manageable for teachers.

We hope that MOP will enrich your physics teaching and will help your students not only to learn more physics and to learn it better, but also to improve their thinking and learning skills. If we had to pick one word to emphasize, it would be *communication*. Two-way communication between the teacher and students is critical to the success of the educational endeavor. No set of fixed materials can ever be the total solution to an educational problem. Only teachers can act flexibly enough to meet all the needs of their students, and only through open dialogue between teachers and students can teachers determine fully the needs of their students, and students receive the feedback they need to remain constructively engaged in the learning process.

*Development of the Minds•On Physics curriculum materials was supported by the National Science Foundation (NSF), under grants MDR-9050213 and ESI-9255713.*

Does Minds*On Physics answer the call of the National Science Education Standards

When the standards say... |
Minds•On Physics replies... |

Science is for all students. | Everyone can learn physics. The MOP program presents physics as an exercise in analyzing and solving problems. |

Learning is an active process. | Since students learn in different ways, MOP offers a wide variety of activities so that every student experiences success. |

Teachers should focus and support inquiries while interacting with students. | MOP minimizes lecturing and maximizes student-student / student-teacher interaction. |

Teachers should orchestrate discourse among students about scientific ideas. | MOP activities and discussion are student-driven; students are active participants in their own learning. |

Achievement data collected should focus on the science content that is most important for students to learn. | MOP advocates a departure from the static, such as memorizing facts, to the dynamic, such as reasoning skill development. |

Equal attention must be given to the assessment of opportunity to learn and to the assessment of student achievement. | MOP activities are a continuous formative assessment of student thinking. |

Assessment tasks should be authentic. | MOP mimics professional science. |

All students should develop abilities necessary to do scientific inquiry. | MOP activities promote individual skills needed to do science, including both operational and critical thinking skills. |

We developed Minds•On Physics with curriculum reform in mind. The program builds upon and expands students' knowledge about the physical world, getting students to think about and do science in a way that is meaningful to them.

Attachment | Size |
---|---|

MOP vs. Standards, Long Version (PDF) | 60.07 KB |

Questons and answers about the Minds*On Physics curriculum

*These questions are loosely based on ones asked by the Chicago Public Schools Board when they were considering adopting the MOP curriculum.*

**How does your program or materials line up with the Illinois Learning Standards or the NRC's National Science Education Standards?**

See our comparison of the Minds•On Physics approach with the NSES (1996). A more detailed comparison can be found in the PDF attachment at the bottom of that page.

**Do you have any data about student achievement in districts that have been using the program for a minimum of two years?**

No, but the evaluation team headed by Allan Feldman said the following in their executive summary based on the beta field-testing:

When the MOP approach is used with the MOP materials as a comprehensive curriculum... students gain access to knowledge and skills that allow them to develop expert-like, concept-based problem solving abilities that are inaccessible with traditional curricula. In addition, students who used MOP regularly showed a greater awareness of their metacognitive process in solving physics problems than did students who used MOP only occasionally. (Feldman & Kropf, MOP Executive Summary, p.2, 7/23/97)

**Can you give us some relevant background about the instructional framework of the materials and the research that guided the materials development?**

The instructional framework for MOP is called *Concept-based Problem Solving*. The approach emphasizes analysis and reasoning over both pure conceptual understanding and pure numerical problem solving. Students spend a lot less time solving problems, but they develop deeper understanding and more robust problem-solving skills.

The developers are researchers in physics education, with credentials in expert-novice studies, metacognition, and bilingual research. The materials were developed using a cognitive framework based on multiple strands of educational research, including misconceptions, schema acquisition, cognitive overload, and the knowledge store and problem-solving techniques of experts and novices.

The approach is described in several sources. For instance, Supplement B of the (MOP) Motion Teacher's Guide is entitled *Concept-based Problem Solving: Combining educational research results and practical experience to create a framework for learning physics and to derive effective classroom practices*. A slightly shorter version can be found under the title *Analysis-based Problem Solving: Making analysis and reasoning the focus of physics instruction*.

**Can you give us a detailed description of the development process, including the names of the primary developers and the pilot/field testing process, and a list of field or pilot test sites?**

The development process can be divided into three phases: piloting, field-testing, and publishing. We started in 1990 with a team of four physics education researchers (UMPERG) and four high school teachers from a range of settings and with a range of skills and experience. The teachers reviewed the module activities drafted by UMPERG, making comments, corrections, and suggestions that were then used to revise the modules before piloting them. The teachers piloted the modules, gave UMPERG more advice about the materials, and allowed UMPERG into their classrooms to see how they were used and to talk to students. At the end of the pilot project in 1992, we had developed and tested 24 modules, covering only about 1/3 of the school year. The accompanying teacher support materials consisted of answers with short explanations to all of the module questions. The modules were developed under the National Science Foundation grant MDR-9050213.

In the field-testing phase (1993-97), we divided the modules into smaller activities that could be started and completed during the same class period. We also began developing additional activities in order to span a full year, and we added a "Student Reader" to summarize the ideas raised in the activities. The teacher support materials became "Answers and Instructional Aids for Teachers" with tidbits such as Preparation for Students, Anticipated Difficulties for Students, and Suggested Points for Class Discussion. We added 30 more teachers in Massachusetts, Tennessee, and Louisiana to field-test the materials, having meetings with local teachers every 6 weeks or so to gather insights and share experiences. Meetings with teachers in Chattanooga, TN and New Orleans, LA occurred less frequently but were just as informative. At the end of this phase, we had field-tested more than 100 activities. These activities were developed under NSF grant ESI-9255713.

In the publishing phase (1997-2003), we organized the activities into a "core" curriculum and a "supplemental" curriculum having three volumes each. The field-tested activities became the core curriculum, and we developed another 80 activities for the supplemental curriculum. We also organized and expanded the existing Answers and Instructional Aids for Teachers into more complete Teacher's Guides, one to accompany each volume of activities, and wrote Teacher's Guides for the three volumes of new activities. The last Teacher's Guide was published earlier this year.

For more detailed information about the actual development process, please refer to our model-based design paradigm as described in section IV of the technical report *ASK-IT/A2L: Assessing Student Knowledge with Instructional Technology*.

UMPERG [as of the writing of MOP --- *ed*] is William Gerace, Jose Mestre, Robert Dufresne, and William Leonard. All four are Physics PhDs with extensive teaching and research experience. They have conducted more than 60 workshops and mini-courses on learning and instruction, have written numerous articles on educational issues, given almost 200 talks on physics instruction, and done more than 70 science demonstration shows for nearly 2000 school children in the U.S. and South Africa. (These shows demonstrate how physics is manifest in everyday situations with common items.)

The pilot sites were in four very different settings. One is an excellent private school in NW Massachusetts. Another is a suburban HS with a diverse student population. A third is an average urban HS in Springfield, MA, with a large, though not predominantly, minority student population, and the fourth is an inner city, bottom-rung, 100% minority, school-of-last-resort for students in Hartford, CT.

The pilot teachers are also very different. One has an Ed.D. from the University of Massachusetts, and has even co-authored his own instructional manual for teachers. He is involved in lots of innovative programs, and is always willing to try something new. The second is a traditional teacher, well trained in physics and not overly creative in his teaching. The third is a biology teacher with almost no content knowledge teaching physics, but he is brilliant in creating group activities, however, and we learned much from him about adapting our materials to group work. The fourth is an energetic and highly adaptable physics and astronomy teacher.

A list of the field-test teachers can be found in the Acknowledgments of any one of the Student Activities books. There are 34 in all. Most are located in Massachusetts, but one cadre was located in and around Chattanooga, TN, and another was located in and around New Orleans, LA.

**How does the program or materials address diversity in the student population?**

Diversity is not limited to ethnic and cultural diversity. Every student has a unique set of skills, past experiences, and approaches, and so, in Minds•On Physics, we show teachers that there are many paths to success and many different ways to do physics. If a student, for example, does not have the algebraic skills to solve a traditional problem, we show how to help that student reason through to an answer. If a school system does not have a large equipment budget, we show them how to think and live and do physics without any expensive equipment.

If you look at MOP, you will see an emphasis on thinking, analyzing, and reasoning, which anyone can be encouraged to do at any age with almost any background. Also, you will see common everyday manipulatives, such as balls, toy cars, and rubber bands, items that students are familiar with and almost any school system can afford.

MOP is activity-based, which means the teacher decides the depth and level of coverage. MOP has been used in many different contexts, such as 8th and 9th grade physical science, 11th and 12th grade college prep physics, as supplementary materials in introductory college physics, and in graduate level teacher preparation courses. There are even a few students I know who have used the "Complex Systems" volume to help them with their Junior level (University) Statistical Physics class.

MOP has been used in schools with large minority student populations in Chattanooga, TN, New Orleans, LA, Springfield, MA, and Hartford, CT, and MOP has recently been adopted by Grand Rapids, MI. MOP has also been used in "bridging" programs for under-prepared black university students in South Africa.

**Have you done an external evaluation of the materials by objective and respected sources?**

The evaluation of Minds•On Physics was done by a team of researchers led by Allan Feldman of the University of Massachusetts School of Education. An executive summary is available.

Attachment | Size |
---|---|

MOP Evaluation Executive Summary | 41.25 KB |

Tables of contents for the books of the MOP series

The MOP curriculum consist of four reusable *Activities & Reader* books for students (paperback, 8.5" x 11"), which together span a complete full year curriculum for high-school physics.

For each of the student books there is an accompanying *Teacher's Guide* (spiral bound, 8.5" x 11"). These includes advice for using the MOP curriculum, answers and instructional aids for every activity in the student book, supplemental discussions on pedagogic practices, and removable, photocopy-ready answer sheets for students to use with the activities.

Activities & Reader (ISBN 0-7872-3927-5, 190 pages)

How to Use This Book *xi*

Acknowledgments *xiii*

- 1 - Looking Ahead
*1* - 2 - Communicating the Position of an Object
*3* - 2A - Communicating the Position of an Object (Alternative Version)
*7* - 3 - Describing Position
*9* - 4 - Using Graphs of Position vs. Time
*15* - 5 - Generating Sketches of Position vs. Time
*19* - 6 - Translating Graphs of Position vs. Time
*23* - 7 - Describing Displacement
*27* - 8 - Describing Velocity
*31* - 9 - Using Graphs of Velocity vs. Time
*35* - 10 - Generating Sketches of Velocity vs. Time
*39* - 11 - Translating Graphs of Velocity vs. Time
*43* - 12 - Relating Strobe Diagrams to Plots of Position vs. Time and Velocity vs. Time
*47* - 13 - Finding and Comparing Velocities
*53* - 14 - Relating Graphs of Position vs. Time and Velocity vs. Time
*57* - 15 - More Relating Graphs of Position vs. Time and Velocity vs. Time
*61* - 16 - Solving Constant-Velocity Problems Using Different Methods
*65* - 17 - Solving Constant-Velocity Problems
*69* - 18 - Recognizing Accelerated Motion
*73* - 19 - Describing Changes in Velocity
*75* - 20 - Recognizing Graphs of Acceleration vs. Time
*81* - 21 - Generating Sketches of Acceleration vs. Time
*85* - 22 - Translating Graphs of Acceleration vs. Time
*87* - 23 - Calculating Average Acceleration
*89* - 24 - Relating Strobe Diagrams to Graphs of Acceleration vs. Time
*93* - 25 - Relating Graphs and Kinematic Functions
*97* - 26 - Relating Kinematic Quantities with Kinematic Functions
*101* - 27 - Relating Graphs of Position, Velocity, and Acceleration vs. Time
*105* - 28 - Comparing Graphs of Velocity vs. Time and Displacement vs. Time
*109* - 29 - Translating Between Different Representations of Accelerated Motion
*111* - 30 - Graphical Representations of Motion: Reflection and Integration
*115* - 31 - Evaluating Procedures for Solving Kinematics Problems
*119* - 32 - Executing Procedures for Solving Kinematics Problems
*125* - 33 - Generating Procedures for Solving Kinematics Problems
*127* - 34 - Solving Constant-Acceleration Problems
*129* - 35 - Summarizing and Structuring Kinematics Ideas
*133*

- 1.0 Introduction
*R1*- six terms used to describe motion
*R1*

- six terms used to describe motion
- 1.1 Position
*R1-5*- Describing the position of an object
*R1-4*- definition of the term
*origin**R1* - units of position: meter (m), kilometer (km), and centimeter (cm)
*R2* - three representations for position
*R2*- magnitude & direction representation
*R2* - component representation
*R3* - directed line segment representation
*R3*

- magnitude & direction representation
- representing the position in two dimensions
*R3*- magnitude & direction
*R3,4* - component representation
*R4* - directed line segment
*R4*

- magnitude & direction
- why we use three different representations
*R4*

- definition of the term
- Using graphs to describe the position of objects moving in one dimension
*R5*

- Describing the position of an object
- 1.2 Displacement
*R6,7*- Introduction
*R6* - Displacement in one dimension
*R6,7*- symbol for displacement: "delta-
*x*"*R6* - definition of displacement
*R6* - an example of displacement in all three representations
*R6,7*

- symbol for displacement: "delta-
- Displacement in two dimensions
*R7*

- Introduction
- 1.3 Velocity
*R8-18*- Introduction
*R8,9*- difference between speed and velocity
*R8* - how we recognize when something has a velocity
*R8* - definition of average velocity (in one dimension)
*R8* - definition of velocity (or instantaneous velocity)
*R9* - definition of speed
*R9*

- difference between speed and velocity
- Representing velocity (in two dimensions)
*R9-11*- using all three representations for velocity
*R10* - how to estimate the components of velocity using a directed line segment
*R11*

- using all three representations for velocity
- Representing velocity at different times (in one dimension)
*R12* - Relationships between graphs of position and velocity
*R12-15*- constant, positive velocity
*R13* - constant, negative velocity
*R13* - changing velocity
*R14* - meaning of the area below velocity vs. time
*R14* - graphs of position vs. time
*R15* - meaning of the slope of position vs. time
*R15*

- constant, positive velocity
- Using algebra to relate position and velocity
*R16,17*- equation for displacement when velocity is constant
*R17* - equation for position vs. time when velocity is constant
*R17*

- equation for displacement when velocity is constant
- Avoiding pitfalls when working with velocity concepts
*R18,19*- definition of average speed
*R18* - why the average speed for a trip is not the average of the speeds during the trip
*R18* - why the average speed for a trip is not the magnitude of the average velocity
*R18,19*

- definition of average speed

- Introduction
- 1.4 Acceleration
*R19-33*- Introduction
*R19-21*- how the term
*acceleration*is used in physics compared to how the term is used in everyday language*R19* - four examples of motion:
*R19-21*- a car moving at constant velocity
*R19* - a car with changing speed but constant direction
*R20* - a car with constant speed but changing direction
*R20* - a thrown ball has changing speed and direction
*R21*

- a car moving at constant velocity

- how the term
- Defining acceleration for straight-line motion (motion in one dimension)
*R21-24*- symbol for acceleration:
*a*_{x}*R21* - definition of average acceleration
*R21* - why "negative acceleration" does
__not__mean "slowing down"*R22,23* - definition of acceleration (or instantaneous acceleration)
*R24*

- symbol for acceleration:
- Representing and interpreting acceleration in one dimension
*R24,25*- using directed line segments for velocity
*R24* - using a number line for velocity
*R25*

- using directed line segments for velocity
- Relationships between graphs of acceleration, velocity, and position (vs. time)
*R26-28*- calculations of the slopes of tangent lines
*R26* - verification that the slope of position vs. time is the velocity
*R26,27* - meaning of the slope of velocity vs. time
*R27* - meaning of the area below acceleration vs. time
*R28*

- calculations of the slopes of tangent lines
- Deriving the kinematic equations for constant acceleration
*R28-33*- acceleration = 0
*R29*- how to find the displacement using a velocity graph
*R29* - equation for the position at time
*t**R29*

- how to find the displacement using a velocity graph
- acceleration <> 0
*R30-33*- how to find velocity using an acceleration graph
*R30* - equation for the velocity at time
*t**R30* - how to find position using a velocity graph
*R31* - equation for the position at time
*t*for constant acceleration*R31* - equation for the squared velocity after displacement "delta-
*x*"*R31* - how to use graphs to solve problems
*R32,33*

- how to find velocity using an acceleration graph

- acceleration = 0

- Introduction
- 1.5 Kinematics
*R34-36*- Introduction
*R34* - Definitions
*R34*- position
*R34* - displacement
*R34* - average velocity
*R34* - velocity
*R34* - speed
*R34* - average speed
*R34* - average acceleration
*R34* - acceleration
*R34*

- position
- Relationships between graphs of motion quantities
*R35*- meaning of the slope of position vs. time
*R35* - meaning of the slope of velocity vs. time
*R35* - meaning of the area below velocity vs. time
*R35* - meaning of the area below acceleration vs. time
*R35* - diagrammatic representation of these relationships
*R35*

- meaning of the slope of position vs. time
- Derived equations relating the motion quantities (for constant acceleration)
*R35*- equation for the velocity at time
*t**R35* - equation for the position at time
*t**R35* - equation for the squared velocity after displacement "delta-
*x*"*R35* - definitions of symbols used in these derived equations
*R35*

- equation for the velocity at time
- Conclusion
*R36*- why problem solving is so difficult
*R36* - how to simplify kinematics problems
*R36* - why understanding motion is so important
*R36*

- why problem solving is so difficult

- Introduction

(ISBN 0-7872-3928-3, 354 pages)

A Letter from the Authors | vii | |

Getting Started with Minds•On Physics | xi | |

Answers & Instructional Aids for Teachers | 1 | |

1 | Looking Ahead | 1 |

2 | Communicating the Position of an Object | 7 |

2A | Communicating the Position of an Object (Alternative Version) | 9 |

3 | Describing Position | 11 |

4 | Using Graphs of Position vs. Time | 17 |

5 | Generating Sketches of Position vs. Time | 23 |

6 | Translating Graphs of Position vs. Time | 29 |

7 | Describing Displacement | 33 |

8 | Describing Velocity | 39 |

9 | Using Graphs of Velocity vs. Time | 45 |

10 | Generating Sketches of Velocity vs. Time | 51 |

11 | Translating Graphs of Velocity vs. Time | 57 |

12 | Relating Strobe Diagrams to Plots of Position vs. Time and Velocity vs. Time | 63 |

13 | Finding and Comparing Velocities | 73 |

14 | Relating Graphs of Position vs. Time and Velocity vs. Time | 77 |

15 | More Relating Graphs of Position vs. Time and Velocity vs. Time | 83 |

16 | Solving Constant-Velocity Problems Using Different Methods | 87 |

17 | Solving Constant-Velocity Problems | 93 |

18 | Recognizing Accelerated Motion | 97 |

19 | Describing Changes in Velocity | 101 |

20 | Recognizing Graphs of Acceleration vs. Time | 109 |

21 | Generating Sketches of Acceleration vs. Time | 115 |

22 | Translating Graphs of Acceleration vs. Time | 121 |

23 | Calculating Average Acceleration | 127 |

24 | Relating Strobe Diagrams to Graphs of Acceleration vs. Time | 133 |

25 | Relating Graphs and Kinematic Functions | 141 |

26 | Relating Kinematic Quantities with Kinematic Functions | 149 |

27 | Relating Graphs of Position, Velocity, and Acceleration vs. Time | 157 |

28 | Comparing Graphs of Velocity vs. Time and Displacement vs. Time | 167 |

29 | Translating Between Different Representations of Accelerated Motion | 173 |

30 | Graphical Representations of Motion: Reflection and Integration | 183 |

31 | Evaluating Procedures for Solving Kinematics Problems | 187 |

32 | Executing Procedures for Solving Kinematics Problems | 191 |

33 | Generating Procedures for Solving Kinematics Problems | 195 |

34 | Solving Constant-Acceleration Problems | 199 |

35 | Summarizing and Structuring Kinematics Ideas | 205 |

Supplement A. Collaborative Group Techniques | A1-A4 | |

Supplement B. Concept-Based Problem Solving: Combining educational research results and practical experience to create a framework for learning physics and to derive effective classroom practices | B1-B26 | |

Supplement C. A Comparison of the Minds•On Physics Approach with the NRC's National Science Education Standards | C1-C10 | |

Answer Sheets | end |

Activities & Reader (ISBN 0-7872-3929-1, 224 pages)

How to Use this Book *xi*

Acknowledgments *xiii*

- 36 - Introducing Vectors
*137* - 37 - Representing Vectors Using Components
*145* - 38 - Changing Vector Representations
*149* - 39 - Adding Vectors
*155* - 40 - Finding Changes in Vector Quantities
*161* - 41 - Recognizing Interactions
*165* - 42 - Identifying Interactions
*169* - 43 - Interpreting Measurements of Forces
*173* - 44 - More Interpreting Measurements of Forces
*179* - 45 - Recognizing Forces in Realistic Situations
*185* - 46 - Comparing Magnitudes of Forces
*191* - 47 - More Comparing Magnitudes of Forces
*195* - 48 - Understanding Friction Forces
*199* - 49 - Calculating Forces Using Empirical Laws
*205* - 50 - Recognizing and Interpreting Free-Body Diagrams
*209* - 51 - Drawing and Using Free-Body Diagrams
*215* - 52 - Analyzing Physical Situations Using Free-Body Diagrams
*223* - 53 - Describing Physical Situations Using Free-Body Diagrams
*227* - 54 - Summarizing and Structuring Interactions
*233* - 55 - Analyzing Physical Situations Using Newton's First and Second Laws
*235* - 56 - More Analyzing Physical Situations Using Newton's First and Second Laws
*243* - 57 - Relating the Forces Exerted on an Object to its Motion
*247* - 58 - Making Distinctions Between Newton's Second and Third Laws
*251* - 59 - Reasoning with Newton's Laws
*257* - 60 - More Reasoning with Newton's Laws
*261* - 61 - Using Newton's Laws to Determine the Magnitudes and Directions of Forces
*267* - 62 - Solving Problems with Newton's Laws
*273* - 63 - Analyzing Forces without Empirical Laws
*277* - 64 - Calculating the Values of Physical Parameters and Quantities
*281* - 65 - Labeling Parts of Solutions and Executing Solution Plans
*285* - 66 - Developing Solution Plans and Solving Force Problems
*293* - 67 - Solving Force Problems: Reflection and Integration
*297* - 68 - Summarizing and Structuring Dynamics
*301* - 69 - Going Beyond Newton's Laws
*303* - 70 - Looking for New Principles
*307*

- 2.0 Introduction
*R37*- What is meant by
*dynamics*?*R37* - Why is acceleration such an important concept?
*R37*

- What is meant by
- 2.1 INTERACTIONS AND FORCES
*R37-46*- Interactions
*R37*- how to tell when two objects are interacting
*R37* - What if the effect is not visible?
*R37*

- how to tell when two objects are interacting
- Forces
*R37,38*- relationship between interactions and forces
*R37* - many different ways to say that two objects are interacting
*R38* - how a force might change during a time interval
*R38*

- relationship between interactions and forces
- Measuring forces
*R38*- explaining why springs are preferred for measuring forces
*R38* - importance of knowing what a scale is actually measuring
*R38*

- explaining why springs are preferred for measuring forces
- Units of force
*R38*- introducing the pound (lb) and the newton (N)
*R38* - converting from one unit of force to another
*R38*

- introducing the pound (lb) and the newton (N)
- Identifying forces
*R39-41*- identifying the objects interacting
*R39* - identifying the type of interaction
*R39,40* - determining the direction of a force
*R40,41*

- identifying the objects interacting
- Empirical force laws
*R41,42*- What is meant by an
*empirical force law*?*R41* - features common to all empirical laws
*R41* - Table I: Summary of the empirical laws for common forces
*R42* - role of magnitude vs. direction in the empirical laws
*R42*

- What is meant by an
- Fundamental laws for forces vs. empirical laws
*R42,43*- What is meant by a fundamental force law?
*R42* - the process of determining empirical force laws
*R42,43* - limitations of empirical laws
*R43*

- What is meant by a fundamental force law?
- Fundamental laws for forces
*R43*- the fundamental forces covered in this course
*R43* - Table II: Summary of the fundamental laws for two common forces
*R43*

- the fundamental forces covered in this course
- Free-body diagrams: A way to help us inventory forces
*R44,45*- the thinking behind a free-body diagram
*R44* - some valid free-body diagrams
*R44* - features of a free-body diagram
*R44,45* - optional features of a free-body diagram
*R45* - guidelines for drawing a free-body diagram
*R45*

- the thinking behind a free-body diagram
- The net force
*R46*- definition of
*net force**R46*

- definition of

- Interactions
- 2.2 NEWTON'S LAWS OF MOTION
*R47-52*- Mass vs. weight
*R47,48*- definition of
*weight**R47* - how to measure the weight of something
*R47* - definition of
*mass**R47* - how to measure the mass of something
*R47* - comparing the mass and the weight on the earth versus on the moon
*R47,48* *gravitational mass*versus*inertial mass**R48*

- definition of
- Newton's three laws of motion
*R48-50*- Newton's first law of motion
*R48*- verbal statement of Newton's 1st law
*R48* - definition of
*net force**R48*

- verbal statement of Newton's 1st law
- Newton's second law of motion
*R49*- verbal statement of Newton's 1st law
*R49* - mathematical statement of Newton's 1st law
*R49* - definitions of
*inertial mass*and*gravitational mass**R49* - definition of
*equilibrium**R49*

- verbal statement of Newton's 1st law
- Newton's third law of motion
*R50*- verbal statement of Newton's 3rd law
*R50* - mathematical statement of Newton's 3rd law
*R50* - relationship between forces and interactions
*R50* - explanation of the terms
*action*and*reaction**R50* - difference between a
*reaction*force and a*balancing*force*R50*

- verbal statement of Newton's 3rd law

- Newton's first law of motion
- Newton's laws and reference frames
*R50,51*- confirming Newton's laws using a constant-velocity frame
*R50* - contradicting Newton's laws using an accelerating frame
*R50* - definition of
*inertial frame**R51*

- confirming Newton's laws using a constant-velocity frame
- Newton's laws and free-body diagrams
*R51,52*- Newton's 2nd law in component form
*R51* - applying the definition of the net force using components
*R52*

- Newton's 2nd law in component form

- Mass vs. weight
- 2.3 DYNAMICS
*R52-60*- An agenda for dynamics
*R52,53* - Kinematics versus dynamics
*R53* - Reasoning with Newton's laws
*R53-56*- equilibrium situations (net force is zero)
*R54,55* - non-equilibrium situations (net force is not zero)
*R56*

- equilibrium situations (net force is zero)
- Solving problems with Newton's laws
*R56-59*- goal of this approach to learning physics
*R56* - importance of analysis and reasoning skills
*R56* - role of analysis and reasoning while problem solving
*R56-58* - overview of problem solving in physics
*R59* - diagrammatic representation of the problem-solving process
*R59* - meaning of the diagrammatic representation
*R59*

- goal of this approach to learning physics
- Summary
*R59* - Limitations of dynamics
*R59,60*- conditions needed to solve dynamics problems
*R59* - some situations in which the motion cannot be determined using dynamics alone
*R60*

- conditions needed to solve dynamics problems
- Conclusion
*R60*

- An agenda for dynamics

- Contact Forces
*A1-4*- Normal force
*A1* - Tension force
*A1* - Spring force (also called Elastic force)
*A2* - Buoyant force
*A2* - Friction forces
*A3*- kinetic
*A3* - static
*A3*

- kinetic
- Air resistance force (also called Drag force)
*A4*

- Normal force
- Action-at-a-distance Forces
*A5,6*- Gravitational force
*A5*- near the surface of the Earth
*A5* - Universal Law of Gravitation
*A5*

- near the surface of the Earth
- Electrostatic force
*A6* - Magnetic force
*A6*

- Gravitational force

(ISBN 0-7872-3930-5, 372 pages)

Overview of the Minds•On Physics Materials | vii | |

How to Use This Book | ix | |

Answers & Instructional Aids for Teachers: | 211 | |

36 | Introducing Vectors | 211 |

37 | Representing Vectors Using Components | 221 |

38 | Changing Vector Representations | 225 |

39 | Adding Vectors | 231 |

40 | Finding Changes in Vector Quantities | 239 |

41 | Recognizing Interactions | 249 |

42 | Identifying Interactions | 255 |

43 | Interpreting Measurements of Forces | 261 |

44 | More Interpreting Measurements of Forces | 267 |

45 | Recognizing Forces in Realistic Situations | 275 |

46 | Comparing Magnitudes of Forces | 283 |

47 | More Comparing Magnitudes of Forces | 289 |

48 | Understanding Friction Forces | 295 |

49 | Calculating Forces Using Empirical Laws | 303 |

50 | Recognizing and Interpreting Free-Body Diagrams | 311 |

51 | Drawing and Using Free-Body Diagrams | 319 |

52 | Analyzing Physical Situations Using Free-Body Diagrams | 327 |

53 | Describing Physical Situations Using Free-Body Diagrams | 335 |

54 | Summarizing and Structuring Interactions | 343 |

55 | Analyzing Physical Situations Using Newton's First and Second Laws | 351 |

56 | More Analyzing Physical Situations Using Newton's First and Second Laws | 365 |

57 | Relating the Forces Exerted on an Object to its Motion | 375 |

58 | Making Distinctions Between Newton's Second and Third Laws | 381 |

59 | Reasoning with Newton's Laws | 389 |

60 | More Reasoning with Newton's Laws | 395 |

61 | Using Newton's Laws to Determine the Magnitudes and Directions of Forces | 403 |

62 | Solving Problems with Newton's Laws | 411 |

63 | Analyzing Forces without Empirical Laws | 421 |

64 | Calculating the Values of Physical Parameters and Quantities | 427 |

65 | Labeling Parts of Solutions and Executing Solution Plans | 433 |

66 | Developing Solution Plans and Solving Force Problems | 445 |

67 | Solving Force Problems: Reflection and Integration | 455 |

68 | Summarizing and Structuring Dynamics | 459 |

69 | Going Beyond Newton's Laws | 465 |

70 | Looking for New Principles | 471 |

Answer Sheets | end |

Activities & Reader (ISBN 0-7872-3931-3, 224 pages)

How to Use this Book *xiii*

Acknowledgments *xv*

- 71 - Investigating Collisions in which Two Objects Stick Together
*313* - 72 - Introducing the Concepts of Impulse and Momentum
*317* - 73 - Using Impulse and Momentum to Solve Constant-Force Problems
*321* - 74 - Analyzing Collisions Using Newton's Third Law
*325* - 75 - Relating Momentum Ideas to One-Body Problem Situations
*331* - 76 - Relating Momentum Ideas to Situations Having Two or More Objects
*335* - 77 - Reasoning with Impulse and Momentum Ideas
*339* - 78 - Solving Problems Using Momentum Principles
*343* - 79 - Summarizing and Structuring Momentum and Impulse Ideas
*347* - 80 - Recording Your Thoughts about Energy
*349* - 81 - Relating Forces to the Motion of Objects
*353* - 82 - Relating Work to Forces and Displacements
*357* - 83 - Recognizing the Presence of Work
*361* - 84 - Comparing the Work Done by Forces
*367* - 85 - Computing the Work Done by Forces
*371* - 86 - Recognizing and Comparing Kinetic Energy
*375* - 87 - Reasoning with Work and Energy Ideas
*381* - 88 - Solving Problems with the Work-Kinetic Energy Theorem
*385* - 89 - Recognizing the Presence of Potential Energy
*389* - 90 - Comparing the Potential Energy
*393* - 91 - Computing the Potential Energy
*399* - 92 - Keeping Track of Energy: The Law of Conservation of Energy
*403* - 93 - Reasoning with Energy Ideas
*411* - 94 - Solving Problems Using Energy Ideas
*415* - 95 - Summarizing and Structuring Energy Ideas
*419* - 96 - Recording Your Ideas about Problem Solutions
*421* - 97 - Recognizing the Appropriate Principle/Law
*425* - 98 - Matching Solution Strategies with Problems
*433* - 99 - Writing and Comparing Solution Strategies
*437* - 100 - Solving One-Principle Problems
*441* - 101 - Solving More Complex Problems
*445* - 102 - Structuring Mechanics
*449*

- 3.0 Introduction
*R61*- What is meant by a conservation law?
*R61* - Why use a conservation law instead of dynamics?
*R61*

- What is meant by a conservation law?
- 3.1 SYSTEMS
*R61*- What is a system?
*R61* - Sizes of systems
*R61*

- What is a system?
- 3.2 MOMENTUM AND IMPULSE
*R62-65*- Impulse
*R62,63*- definition of impulse for constant force
*R62* - units for impulse: N-s
*R62* - how to calculate impulse for a given force and time interval
*R62,63* - definition of net impulse for constant net force
*R63* - how to calculate net impulse for constant net force
*R63*

- definition of impulse for constant force
- Momentum
*R64,65*- definition of momentum for single bodies
*R64* - how to calculate the momentum
*R64* - units for momentum: kg-m/s
*R64* - what momentum means in some common situations
*R64* - how to find the
__change__in momentum*R64,65*

- definition of momentum for single bodies

- Impulse
- 3.3 TWO PRINCIPLES FOR DESCRIBING PHYSICAL SYSTEMS AND SOLVING PROBLEMS
*R66-70*- Impulse-Momentum Theorem
*R66,67*- comparing the net impulse and the change in momentum
*R66* - equivalence of the units for impulse and the units for momentum
*R66* - statement of the Impulse-Momentum Theorem for single bodies
*R66*

- comparing the net impulse and the change in momentum
- Conservation of Momentum for two-body systems
*R68-70*- using Newton's third law to understand collisions
*R68* - using the Impulse-Momentum Theorem to understand collisions
*R69* - statement of Conservation of Momentum for no net force on system
*R69* - definition of
*total*momentum*R69* - situations in which total momentum is only
__approximately__conserved*R69,70*

- using Newton's third law to understand collisions

- Impulse-Momentum Theorem
- 3.4 USING MOMENTUM IDEAS AND PRINCIPLES TO ANALYZE SITUATIONS AND SOLVE PROBLEMS
*R70-79*- Reasoning with momentum ideas
*R70-74*- situations involving a net impulse
*R70-73*- using the Impulse-Momentum Theorem when there is a net impulse
*R71* - looking at the change in momentum
*R71* - making reasonable assumptions before making comparisons
*R72* - using limiting cases to make comparisons
*R72* - effect of mass on an object's response to an interaction
*R73*

- using the Impulse-Momentum Theorem when there is a net impulse
- situations in which the net impulse is zero or very close to zero
*R73,74*- using Conservation of Momentum when the impulse is small
*R74* - Conservation of Momentum is a vector equation
*R74*

- using Conservation of Momentum when the impulse is small

- situations involving a net impulse
- Solving problems with momentum ideas
*R75-78*- using the Impulse-Momentum Theorem to solve problems
*R75,76*- two different ways of using the Impulse-Momentum Theorem
*R75* - Impulse-Momentum Theorem for constant net force
*R75* - four types of quantities: forces, time intervals, masses, velocities
*R75* - representation of problem solving using the Impulse-Momentum Theorem
*R76*

- two different ways of using the Impulse-Momentum Theorem
- using Conservation of Momentum to solve problems
*R76-78*- four common steps for solving Conservation of Momentum problems
*R76* - Conservation of Momentum is a vector equation
*R77,78* - representation of problem solving using Conservation of Momentum
*R78*

- four common steps for solving Conservation of Momentum problems

- using the Impulse-Momentum Theorem to solve problems
- Summary of momentum ideas and principles
*R79*- one new
*state*quantity: momentum**p***R79* - two new
*process*quantities: impulse**J**, and__change__in momentum D**p***R79* - two new physical principles: the Impulse-Momentum Theorem and Conservation of Momentum
*R79* - new energy ideas:
*work, kinetic energy, potential energy**R79* - limitations of momentum ideas
*R79*

- one new

- Reasoning with momentum ideas
- 3.5 WORK AND KINETIC ENERGY
*R80-90*- Definition of work
*R80-84*- What factors affect the way a force changes the speed of something?
*R80* - definition of work for a constant force using the component of the force parallel to the displacement
*R80* - work is a scalar quantity
*R81* - units for work: J (joule)
*R81* - calculating the work done by a constant force
*R81* - how the work done can be negative
*R81* - What happens when the force is perpendicular to the displacement?
*R81* - circumstances when a different definition of work is needed
*R82* - definition of work for a constant force using the component of the displacement parallel to the force
*R82* - definition of total work
*R83,84*

- What factors affect the way a force changes the speed of something?
- Calculating the work done by common forces
*R84-89*- work done by the gravitational force
*R84*- depends on the mass, the gravitational constant (
*g*), and the__change__in height*R84* - why there is a minus sign in the expression
*R84*

- depends on the mass, the gravitational constant (
- work done by the normal force
*R85,86*- why the normal force often does no work on an object
*R85* - situations in which the normal force does work on an object
*R85* - the
__total__work done by the normal force is always zero*R85* - how the normal force can do no work even when it delivers an impulse
*R86*

- why the normal force often does no work on an object
- work done by the tension force
*R86,87*- why the tension force often does no work on an object
*R86* - situations in which the tension force does work
*R86,87* - the
__total__work done by the tension force is always zero*R87*

- why the tension force often does no work on an object
- work done by the friction force (static and kinetic)
*R88*- the static friction force can do work on isolated objects
*R88* - the static friction force can do no
__total__work*R88* - why we cannot calculate the work done by kinetic friction
*R88*

- the static friction force can do work on isolated objects
- work done by the spring force
*R89*- using a graph of force vs. displacement to find the work done
*R89* - the graph of force vs. displacement is often a straight line
*R89*

- using a graph of force vs. displacement to find the work done

- work done by the gravitational force
- Kinetic energy
*R90,91*- What changes when total work is done on an object?
*R90* - definition of kinetic energy
*R90* - circumstances under which the kinetic energy changes
*R91* - definition of
__total__kinetic energy*R91*

- What changes when total work is done on an object?

- Definition of work
- 3.6 TWO MORE PRINCIPLES FOR DESCRIBING PHYSICAL SYSTEMS AND SOLVING PROBLEMS
*R92-99*- Work-Kinetic Energy Theorem
*R92-94*- Statement of the Work-Kinetic Energy Theorem
*R92* - depends on the
__total__work and the__change__in__kinetic__energy*R92* - statement of the Work-Kinetic Energy Theorem for a system of objects
*R92* - depends on the total work and the change in
__total__kinetic energy*R92* - this is a scalar equation
*R92* - using the Work-Kinetic Energy Theorem to find the speed of something
*R92,93* - sometimes the forces doing work are hard to determine
*R94* - more reasons why we cannot calculate the work done by kinetic friction
*R94*

- Statement of the Work-Kinetic Energy Theorem
- Conservation of Energy
*R95-99*- statement of the Law of Conservation of Energy
*R95* - why we need two new kinds of energy:
*potential energy*and*microscopic energy**R95*

- statement of the Law of Conservation of Energy
- Potential energy
*R95-98*- change in gravitational potential energy
*R95* - gravitational potential energy for objects near the surface of celestial bodies
*R95* - using a reference height to determine the gravitational potential energy
*R95* - gravitational potential energy does not depend upon motion
*R96* - gravitational potential energy can be negative
*R96* - finding the potential energy stored in a spring
*R97* - factors affecting the spring potential energy
*R97,98* - the spring potential energy is always positive
*R98*

- change in gravitational potential energy
- Microscopic vs. macroscopic energy
*R98,99*- definitions of the microscopic and macroscopic realms
*R98* - how energy is contained in the microscopic realm
*R98,99* - definition of total energy
*R99* - Law of Conservation of Energy
*R99*

- definitions of the microscopic and macroscopic realms

- Work-Kinetic Energy Theorem
- 3.7 USING ENERGY IDEAS AND PRINCIPLES TO ANALYZE SITUATIONS
*R100-105*- Analyzing situations using the Work-Kinetic Energy Theorem
*R100,101*- whenever the kinetic energy of something changes, work is done
*R100* - difficulties in identifying the forces actually doing work
*R100,101* - similarities and differences between momentum and kinetic energy
*R101*

- whenever the kinetic energy of something changes, work is done
- Analyzing situations using Conservation of Energy
*R102-106*- why the law is not particularly useful without modification
*R102* - Work-Energy Theorem (for a system of objects)
*R102* - definition of
*external*work*R102* - different ways of looking at the same situation
*R102-104* - using dynamics and kinematics to analyze a situation before applying Conservation of Energy
*R104* - where the energy goes during a collision
*R104,105* - change in microscopic energy due to friction
*R105* - different situations that may be used to derive the change in microscopic energy due to friction
*R105* - change in microscopic energy due to air resistance
*R106*

- why the law is not particularly useful without modification

- Analyzing situations using the Work-Kinetic Energy Theorem
- 3.8 USING ENERGY IDEAS AND PRINCIPLES TO SOLVE PROBLEMS
*R106-113*- Solving problems using the Work-Kinetic Energy Theorem
*R106-109*- two procedures for solving problems
*R106-108* - representation of problem solving using the Work-Kinetic Energy Theorem
*R108,109*

- two procedures for solving problems
- Solving problems using Conservation of Energy
*R109-113*- similarities and differences between the Work-Kinetic Energy Theorem and the Work-Energy Theorem
*R109* - problems in which the total work done by external forces is zero or negligibly small
*R110,111* - problem in which the total work done by external forces in non-zero
*R112* - why the Work-Energy Theorem is how we apply Conservation of Energy to a system of objects
*R113* - representation of problem solving using Conservation of Energy
*R113*

- similarities and differences between the Work-Kinetic Energy Theorem and the Work-Energy Theorem
- Summary of energy ideas and principles
*R113*- many new state quantities: kinetic, potential, and microscopic energy
*R113* - many new process quantities: work, changes in state quantities
*R113* - one new physical law: Conservation of Energy
*R113* - two new problem-solving principles: the Work-Kinetic Energy Theorem and the Work-Energy Theorem
*R113*

- many new state quantities: kinetic, potential, and microscopic energy
- Summary of conservation laws
*R113-114*- reasons for using conservation laws
*R113* - how scientists apply conservation laws to new situations
*R114* - what we will do as we study new areas of physics
*R114*

- reasons for using conservation laws

- Solving problems using the Work-Kinetic Energy Theorem

- 4.0 Introduction
*R115*- Some questions you might ask yourself before solving a problem
*R115* - Why a conceptual analysis should precede equation manipulation
*R115*

- Some questions you might ask yourself before solving a problem
- 4.1 A PHYSICIST'S VIEW OF MECHANICS
*R116-121*- Explanation
*R116*- What is meant by a "view of mechanics"
*R116* - what is meant by an "organizational structure"
*R116* - what motivates a physicist's organizational structure
*R116*

- What is meant by a "view of mechanics"
- Prioritizing ideas in mechanics
*R116-120*- chronological list of many of the physics concepts learned so far
*R116* *physical principles*, the most widely useful ideas in physics*R117**concepts*, the ideas needed to understand principles*R117**equations*, the relationships needed to apply concepts and principles (*physical laws*,*definitions*,*empirical laws*, and*derived relations*)*R117,118*- a priority scheme for physics ideas, with examples
*R118,119* - other ideas relevant for solving problems (mathematical principles, operations, and problem-solving techniques)
*R119,120*

- chronological list of many of the physics concepts learned so far
- Interconnecting ideas in mechanics
*R121*- using concepts to organize knowledge
*R121*

- using concepts to organize knowledge

- Explanation
- 4.2 CONCEPT-BASED PROBLEM SOLVING
*R121-126*- How to
__start__solving a problem*R121-123*- the first three steps of concept-based problem solving
*R121,122*- step 1: sort the principles
*R121,122* - step 2: choose a principle
*R122* - step 3: apply the chosen principle and solve for the unknown
*R122*

- step 1: sort the principles
- solution to the sample problem
*R122,123*

- the first three steps of concept-based problem solving
- How to
__finish__solving a problem*R124-126*- four suggestions for efficient and effective problem solving
*R124,125*- create sketches and diagrams
*R124* - count the number of equations and unknowns
*R124* - challenge your assumptions
*R124,125* - check your answer
*R125,126*

- create sketches and diagrams

- four suggestions for efficient and effective problem solving
- Conclusion
*R126*- representation of the concept-based problem-solving approach
*R126*

- representation of the concept-based problem-solving approach

- How to

(ISBN 0-7872-3932-1, 380 pages)

Overview of the Minds•On Physics Materials | vii | |

How to Use This Book | ix | |

Answers & Instructional Aids for Teachers | 483 | |

71 | Investigating Collisions in which Two Objects Stick Together | 483 |

72 | Introducing the Concepts of Impulse and Momentum | 491 |

73 | Using Impulse and Momentum to Solve Constant-Force Problems | 497 |

74 | Analyzing Collisions Using Newton's Third Law | 507 |

75 | Relating Momentum Ideas to One-Body Problem Situations | 517 |

76 | Relating Momentum Ideas to Situations Having Two or More Objects | 525 |

77 | Reasoning with Impulse and Momentum Ideas | 535 |

78 | Solving Problems Using Momentum Principles | 543 |

79 | Summarizing and Structuring Momentum and Impulse Ideas | 553 |

80 | Recording Your Thoughts about Energy | 561 |

81 | Relating Forces to the Motion of Objects | 567 |

82 | Relating Work to Forces and Displacements | 575 |

83 | Recognizing the Presence of Work | 581 |

84 | Comparing the Work Done by Forces | 589 |

85 | Computing the Work Done by Forces | 597 |

86 | Recognizing and Comparing Kinetic Energy | 605 |

87 | Reasoning with Work and Energy Ideas | 615 |

88 | Solving Problems with the Work—Kinetic Energy Theorem | 625 |

89 | Recognizing the Presence of Potential Energy | 635 |

90 | Comparing the Potential Energy | 641 |

91 | Computing the Potential Energy | 651 |

92 | Keeping Track of Energy: The Law of Conservation of Energy | 659 |

93 | Reasoning with Energy Ideas | 671 |

94 | Solving Problems Using Energy Ideas | 685 |

95 | Summarizing and Structuring Energy Ideas | 699 |

96 | Recording Your Ideas about Problem Solutions | 711 |

97 | Recognizing the Appropriate Principle/Law | 715 |

98 | Matching Solution Strategies with Problems | 725 |

99 | Writing and Comparing Solution Strategies | 735 |

100 | Solving One-Principle Problems | 745 |

101 | Solving More Complex Problems | 753 |

102 | Structuring Mechanics | 765 |

Answer Sheets | end |

Activities & Reader (ISBN 0-7872-5412-6, 207 pages)

How to Use this Book *xv*

Acknowledgments *xvii*

- FF·1 - Exploring Models of Electromagnetism
*1* - FF·2 - Using a Model to Interpret, Explain, and Predict
*7* - FF·3 - Investigating Electrical Properties of Materials
*13* - FF·4 - Reasoning with a Model for Electrical Interactions
*17* - FF·5 - Exploring the Magnetic Interaction
*21* - FF·6 - Modeling the Magnetic Properties of Materials
*25* - FF·7 - Modeling the Magnetic Properties of Moving Charges
*29* - FF·8 - Reasoning with a Model for Magnetic Interactions
*35* - FF·9 - Exploring the Gravitational Interaction
*39* - FF·10 - Exploring the Idea of Weight
*43* - FF·11 - Distinguishing Mass and Weight
*47* - FF·12 - Modeling Universal Gravitation
*51* - FF·13 - Using a Mathematical Model for the Electric Force
*55* - FF·14 - Applying Coulomb's Law to Continuous Distributions of Charge
*59* - FF·15 - Estimating Electric Forces Using Coulomb's Law
*65* - FF·16 - Reasoning with Coulomb's Law
*69* - FF·17 - Developing an Empirical Force Law for Magnets
*73* - FF·18 - Using the Universal Law of Gravitation
*79* - FF·19 - Applying Universal Gravitation to Large-Scale Objects
*83* - FF·20 - Reasoning with Universal Gravitation
*87* - FF·21 - Mapping Magnetic Fields
*91* - FF·22 - Representing the Electric Field
*97* - FF·23 - Representing the Electric Field as a Vector Field
*101* - FF·24 - Investigating the Gravitational Field
*107* - FF·25 - Representing Vector Fields Using Field Line Diagrams
*111* - FF·26 - Applying Newton's Laws
*117* - FF·27 - Applying Work and Energy Ideas
*121* - FF·28 - Solving Problems Using Work and Energy Ideas
*127* - FF·29 - Summarizing and Structuring the Fundamental Forces
*131*

- 0. Introduction
*R1*- what is meant by a
*fundamental force**R1* - a list of the fundamental forces
*R1* - some examples of what the fundamental forces are responsible for
*R1* - the organization of the Reader
*R1*

- what is meant by a
- 1. QUALITATIVE DESCRIPTIONS OF FUNDAMENTAL FORCES
*R1-20*- 1.1. Modeling interactions
*R2*- what is meant by the term
*model**R2* - goal of a model
*R2* - graphic representation of modeling
*R2*

- what is meant by the term
- 1.2. Electric phenomena
*R2,3*- examples of electric phenomena
*R2* - table showing how rubbed objects interact with each other
*R3* - introducing
*electric charge*to explain pattern of electric phenomena*R3* - defining which objects are said to be
*positive*, which are*negative*, and which are*neutral**R3*

- examples of electric phenomena
- 1.3. Reasoning about electric interactions
*R4*- an example showing how we can predict the behavior of something
*R4* - an example showing the limitations of our current model
*R4*

- an example showing how we can predict the behavior of something
- 1.4. A simplified model of electric interactions
*R4-6*- goal of our simplified model
*R4* - assumption 1: All matter is made up of sub-microscopic particles
*R5* - assumption 2: These particles have mass and charge
*R5* - assumption 3: "Like" charges repel; "opposite" charges attract; neutral particles do not interact
*R5* - assumption 4: Everyday objects are neutral
*R6* - assumption 5: Charges can be transferred
*R6* - assumption 6: Electric interactions occur when one or both objects have excess charge
*R6* - assumption 7: Charge is
*conserved**R6* - assumption 8: The mass of sub-microscopic particles is very small
*R6* - assumption 9: When styrofoam is rubbed with fur, the fur is defined to be positive, and the styrofoam is defined to be negative
*R6*

- goal of our simplified model
- 1.5. Applying the simplified model of electric interactions
*R7*- An example showing how the model can predict the behavior of something
*R7*

- An example showing how the model can predict the behavior of something
- 1.6. The atomic model of matter
*R7,8*- types of charge on the proton, neutron, and electron
*R7* - how the atomic model will and will not be used
*R8*

- types of charge on the proton, neutron, and electron
- 1.7. A model of the electrical properties of materials
*R8,9*- goal of our model of electrical properties of materials
*R8* - assertion 1: Only electrons can be transferred by rubbing
*R8* - assertion 2: Excess electrons on a conductor flow easily
*R8* - why some electrical demonstrations give inconsistent results
*R8* - assertion 3: Excess electrons on an insulator do not flow very easily
*R9* - assertion 4: Some electrons in a conductor are relatively free to move
*R9* - conductors exchange electrons on contact
*R9* - assertion 5: Most electrons in an insulator are not relatively free to move
*R9* - assertion 6: The strength of the electric force depends on charge separation
*R9*

- goal of our model of electrical properties of materials
- 1.8. Applying the atomic model of electric interactions
*R10,11*- explaining why neutral objects are attracted to charged objects
*R10* - predicting the charges on pie plates
*R11*

- explaining why neutral objects are attracted to charged objects
- 1.9. Magnetic phenomena
*R11,12*- what is meant by a
*permanent magnet**R11* - what is meant by the
*poles*of a magnet*R11* - what is meant by the
*North*(*N*) and*South*(*S*) poles of a magnet*R11* - table showing how different materials interact magnetically
*R12* - other properties of interacting materials
*R12*

- what is meant by a
- 1.10 Modeling the magnetic interaction
*R12-14*- what is meant by a
*nanomagnet**R13* - assumption 1: All matter is made up of tiny nanomagnets
*R13* - assumption 2: "Like" poles repel; "opposite" poles attract
*R13* - assumption 3: Every material's nanomagnets have a characteristic strength
*R13* - what is meant by
*magnetic materials**R13* - assumption 4: The interaction of two nanomagnets depends on their strengths
*R13* - assumption 5: The interaction of two nanomagnets depends on their separation
*R13* - what is meant by
*non-magnetic materials**R13* - how these assumptions are applied to different materials
*R13* - rough depictions of the nanomagnets in non-magnetic materials, magnetic materials, and permanent magnets
*R14* - what is meant by a
*magnetic domain**R14*

- what is meant by a
- 1.11 Applying our simplified model of magnetic interactions
*R14*- Examples of how to apply this model of magnetic interactions
*R14*

- Examples of how to apply this model of magnetic interactions
- 1.12 An atomic model of magnetic interactions
*R15*- reasons we need to go to the atomic model
*R15* - two moving charges are needed for the magnetic interaction
*R15* - how to go from moving charges to nanomagnets
*R15*

- reasons we need to go to the atomic model
- 1.13 Applying the atomic model of magnetic interactions
*R16*- one more assumption: the strength of a nanomagnet is due primarily to an atom's orbiting electrons
*R16* - examples of how to apply the atomic model of magnetic interactions
*R16*

- one more assumption: the strength of a nanomagnet is due primarily to an atom's orbiting electrons
- 1.14 "Local" gravitation
*R17,18*- what is meant by
*local gravitation**R17* - how we know that gravitation is caused by the Earth
*R17* - what is meant by "local" gravitation on the Moon
*R18*

- what is meant by
- 1.15 Weight
*R18*- how weight might appear to be different for different observers
*R18* - definition of the term
*weight**R18* - why a scale sometimes cannot be used to determine weight
*R18* - why air has weight
*R18*

- how weight might appear to be different for different observers
- 1.16 Mass vs. weight
*R19*- differences between
*mass*and*weight**R19*

- differences between
- 1.17 "Universal" gravitation
*R19,20*- what is meant by
*Universal gravitation**R19* - gravitational force as a function of position assuming the Earth has a uniform density
*R19* - comparison of the gravitational forces exerted by the Earth and the Moon
*R20* - why the local gravitational constant on the Moon is 1/6 that on the Earth
*R20* - summary of gravitation
*R20*

- what is meant by

- 1.1. Modeling interactions
- 2. MATHEMATICAL DESCRIPTIONS OF FUNDAMENTAL FORCES
*R21-33*- 2.1. Coulomb's law for electric forces
*R21,22*- what is meant by a
*point charge**R21* - mathematical description of Coulomb's law
*R21* - how to find the direction of the electric force
*R21* - MKS unit of charge (the
*Coulomb*, C)*R22* - charges of the proton and electron
*R22* - an example of how to apply Coulomb's law
*R22*

- what is meant by a
- 2.2. The Superposition Principle
*R22,23*- why we need the Superposition Principle
*R22* - verbal description of the Superposition Principle
*R22* - an example showing how to apply the Superposition Principle
*R23*

- why we need the Superposition Principle
- 2.3. Applying Coulomb's law to non-point objects
*R24*- force law when objects are far apart
*R24* - how to treat objects close together
*R24*

- force law when objects are far apart
- 2.4. Reasoning with Coulomb's law
*R25,26*- a convenient unit of charge is the
*microCoulomb*(µC)*R25* - 3 examples showing how to reason using Coulomb's law
*R25,26*

- a convenient unit of charge is the
- 2.5. Universal law of gravitation
*R27,28*- mathematical description of the Universal law of gravitation
*R27* - how to find the direction of the gravitational force
*R27* - an example showing how to apply the Universal law of gravitation
*R27* - an example showing how to apply the Superposition Principle
*R28*

- mathematical description of the Universal law of gravitation
- 2.6. Applying Universal gravitation to non-point objects
*R28,29*- applying Universal gravitation when objects are far apart
*R28* - applying Universal gravitation when an object is close to a celestial body
*R28,29* - what is meant by a
*shell**R28* - force law when object is outside the mass shell
*R29* - force law when object is inside the mass shell
*R29* - how to apply these results to celestial bodies such as the Earth and Moon
*R29*

- applying Universal gravitation when objects are far apart
- 2.7. Astronomical data
*R30*- mass, average radius, average density,
*g*on its surface, average orbital radius, and orbital period for the Earth, the Moon, and the Sun*R30* - an example of how to use astronomical data
*R30*

- mass, average radius, average density,
- 2.8. Deciding how to apply the Universal law of gravitation
*R30,31*- 3 general methods for applying the Universal law of gravitation
*R30,31* - an example showing how these methods apply to 6 situations
*R31*

- 3 general methods for applying the Universal law of gravitation
- 2.9. Reasoning with Universal gravitation
*R32,33*- examples showing how to reason using Universal gravitation
*R32,33*

- examples showing how to reason using Universal gravitation
- 2.10 The magnetic interaction
*R33*- why we cannot provide a mathematical description of the magnetic interaction
*R33* - some features you should still know about the magnetic interaction
*R33*

- why we cannot provide a mathematical description of the magnetic interaction

- 2.1. Coulomb's law for electric forces
- 3. FIELDS
*R34-45*- some of the different ways the term
*field*is used*R34* - 3.1. Scalar vs. vector fields
*R34*- what is meant by a
*scalar field**R34* - what is meant by a
*vector field**R34* - temperature is a good example of a scalar field
*R34* - velocity of air currents is a good example of a vector field
*R34* *vector field diagram*for air currents in a certain region of space*R34*

- what is meant by a
- 3.2. Fields for fundamental forces
*R35*- why we introduce fields for fundamental forces
*R35* - how a fundamental field is defined: in terms of the force exerted on an object
*R35* - what creates what types of fields
*R35*

- why we introduce fields for fundamental forces
- 3.3. The electric field
*R36*- force on point charge
*q*due to electric field**E***R36* - definition of the electric field
*R36* - using Coulomb's law to find the electric field created by a point charge
*R36* - finding the direction of the electric field
*R36* - how the mutual forces can be the same even though the fields are different
*R36*

- force on point charge
- 3.4. Electric field for multiple point charges
*R37*- an example of how to find the electric field for two point charges
*R37* - vector field diagrams for the "dipole" and "dicharge" distributions of charge
*R37*

- an example of how to find the electric field for two point charges
- 3.5. Electric field for a spherical shell of charge
*R38*- electric field inside a shell of charge
*R38* - electric field outside a shell of charge
*R38* - finding the direction of the electric field outside a shell of charge
*R38* - an example showing how to find the electric field on a rubber ball
*R38*

- electric field inside a shell of charge
- 3.6. The gravitational field
*R39*- why we use the same symbol for "local" and "Universal" gravitation
*R39* - definition of the gravitational field
*R39* - gravitational field created by a point mass
*R39* - how to find the direction of the gravitational field
*R39*

- why we use the same symbol for "local" and "Universal" gravitation
- 3.7. Gravitational field for non-point masses
*R39,40*- using shells to find the gravitational field for a celestial body
*R39* - sketch of gravitational field strength
*g*vs. distance from the center of the Earth*R40* - finding and verifying the location between the Earth and the Moon where the gravitational field is zero
*R40*

- using shells to find the gravitational field for a celestial body
- 3.8. The magnetic field
*R41*- why we use a compass needle to determine the direction of the magnetic field
*R41* - magnetic field for a long, straight wire
*R41* - magnetic field for a loop of wire
*R41*

- why we use a compass needle to determine the direction of the magnetic field
- 3.9. Finding the magnetic field for other arrangements of current-carrying wire
*R42*- magnetic field for two parallel wires, with currents moving in opposite directions
*R42* - magnetic field for a coil of wire
*R42*

- magnetic field for two parallel wires, with currents moving in opposite directions
- 3.10 Force on a point charge moving through a magnetic field
*R42,43*- diagram showing the orientations of the velocity
**v**, magnetic field**B**, and magnetic force**F**_{}*m**R42* - 2 mathematical expressions for the magnetic force on charge
*q**R43* - finding the direction of the magnetic force
*R43* - why we cannot write an expression for the magnetic field
**B**created by a moving point charge*R43*

- diagram showing the orientations of the velocity
- 3.11 Limitations of vector field diagrams
*R43*- many reasons why vector field diagrams are sometimes not the best way to represent fields
*R43* - an example using the "dipole" arrangement of charges
*R43*

- many reasons why vector field diagrams are sometimes not the best way to represent fields
- 3.12 Field line diagrams
*R44*- what is meant by a
*field line**R44* - how to find the direction of the vector field using a field line
*R44* - field line diagrams are 3 dimensional
*R44* - drawing showing the field lines near a positive point charge
*R44* - how to find the comparative strength of the vector field using the density of field lines
*R44* - why we usually draw field line diagrams in only 2 dimensions
*R44* - limitations of the 2-dimensional field line diagram
*R44*

- what is meant by a
- 3.13 Interpreting field line diagrams
*R44,45*- an example using a pair of point charges
*R44,45* - description of the field line diagram
*R44* - analysis of the field line diagram
*R44,45* - actual charge distribution used in this example
*R45*

- an example using a pair of point charges
- 3.14 Reasoning with field line diagrams
*R45*- 3 conclusions that can be reached through reasoning
*R45*- - Field lines do not cross each other
*R45* - - Field lines are not the paths of objects
*R45* - - The field is not strongest near field lines
*R45*

- - Field lines do not cross each other

- 3 conclusions that can be reached through reasoning

- some of the different ways the term
- 4. REASONING AND SOLVING PROBLEMS USING PHYSICAL LAWS
*R46-53*- a list of the useful concepts, principles, and models presented so far
*R46* - 4.1. Reasoning with Newton's laws
*R46-48*- how this part of the Reader will be different from earlier parts involving forces
*R46* - an example involving Newton's 2nd and 3rd laws, as well as momentum conservation
*R47* - an example involving our model of materials
*R47* - an example showing how diagrams can be useful
*R48*

- how this part of the Reader will be different from earlier parts involving forces
- 4.2. Solving problems using Newton's laws
*R48,49*- an example involving the magnetic interaction
*R48,49*

- an example involving the magnetic interaction
- 4.3. Reasoning with energy ideas
*R49-51*- table showing the major energy principles, with related concepts and their definitions
*R49* - an example involving the Work-Energy Theorem
*R50* - an example involving the Work-Kinetic Energy Theorem
*R50*

- table showing the major energy principles, with related concepts and their definitions
- 4.4. Solving problems using energy ideas
*R51-53*- the procedure for determining potential energy
*R51* - some common reference points
*R51* - finding the potential energy stored in the field of two point charges
*R51* - choosing the reference point for two point charges
*R51* - mathematical expression for the potential energy for two point charges
*R51* - mathematical expression for the potential energy for two point masses
*R52* - an example showing how to apply gravitational and electric potential energy
*R52,53* - 5 common steps needed to solve problems using energy ideas
*R53*

- the procedure for determining potential energy

- a list of the useful concepts, principles, and models presented so far

(ISBN 0-7872-3934-8, 458 pages)

*Sorry, but we haven't posted the table of contents for this volume (yet). Contact Bill Leonard for assistance.*

Activities & Reader (ISBN 0-7872-5411-8, 172 pages)

How to Use this Book *xv*

Acknowledgments *xvii*

- AT·1 - Exploring Ideas About Circular Motion
*1* - AT·2 - Finding Acceleration for Circular Motion
*5* - AT·3 - Finding Radial Acceleration for Circular Motion
*9* - AT·4 - Finding Tangential Acceleration for Circular Motion
*13* - AT·5 - Reasoning About Circular Motion
*15* - AT·6 - Solving Problems in Circular Motion
*19* - AT·7 - Exploring Ideas About Projectile Motion
*23* - AT·8 - Relating Kinematic Quantities for Two-Dimensional Motion
*29* - AT·9 - Reasoning About Projectile Motion
*35* - AT·10 - Solving Problems in Projectile Motion
*39* - AT·11 - Solving Problems in Two-Dimensional Motion
*43* - AT·12 - Exploring Ideas About Relative Motion
*47* - AT·13 - Exploring Relative Motion in Two Dimensions
*51* - AT·14 - Reasoning About Relative Motion
*55* - AT·15 - Solving Problems in Relative Motion
*59* - AT·16 - Graphing Rotational Motion
*63* - AT·17 - Introducing Rotational Kinematics
*67* - AT·18 - Solving Rotational Kinematics Problems
*71* - AT·19 - Introducing Rotational Dynamics
*75* - AT·20 - Solving Rotational Dynamics Problems
*79* - AT·21 - Identifying Energy in Rotational Systems
*83* - AT·22 - Solving Problems with Energy in Rotational Systems
*87* - AT·23 - Solving Problems in Rotational Motion
*91*

- Chapter 1. Circular, Projectile & Relative Motion
- 3 independent sections: circular motion, projectile motion & relative motion
*R1* - 1.1. CIRCULAR MOTION
*R1-10*- types of situations covered by
*circular motion**R1,2* - 1.1.1. Uniform circular motion
*R2-4*- what is meant by "uniform" circular motion
*R2* - factors affecting acceleration: speed and radius of circle
*R2* - starting with the definition of acceleration
*R2* - diagram showing the change in velocity [delta]v for a small time period
*R3* - table showing the average acceleration for smaller and smaller time periods
*R3* - 1 effect of doubling the radius of the circular path
*R3* - 2 effects of doubling the speed of the ball
*R3* - magnitude of the acceleration for uniform circular motion
*R4* - direction of the acceleration for uniform circular motion
*R4*

- what is meant by "uniform" circular motion
- 1.1.2. Newton's laws and uniform circular motion
*R4*- relationship between net force and acceleration
*R4*

- relationship between net force and acceleration
- 1.1.3. Non-uniform circular motion
*R5,6*- what is meant by "non-uniform" circular motion
*R5* - definition of the
*radial*component of acceleration*R5* - definition of the
*tangential*component of acceleration*R5* - magnitude of the
**radial component**of acceleration for motion along__any__circle*R5* - direction of the radial component of acceleration
*R5* - magnitude of the
**tangential component**of acceleration for motion along__any__circle*R5* - direction of the tangential component of acceleration
*R5* - finding the forces responsible for the radial and tangential accelerations
*R5,6*

- what is meant by "non-uniform" circular motion
- 1.1.4. Motion along a curved path
*R6,7*- importance of finding circles that match the curvature of the path
*R6* - radial acceleration points toward the
*center of curvature**R6* *radius of curvature*is the radius of the matching circle*R7*- magnitude of the
**radial component**of acceleration for motion along__any__path*R7* - direction of the radial component of acceleration
*R7*

- importance of finding circles that match the curvature of the path
- 1.1.5. Reasoning with circular motion ideas
*R7-9*- only 2 new "big ideas" in circular motion
*R7* - integrating old ideas into new situations
*R7* - using a free-body diagram to analyze circular motion
*R8* - using energy ideas to analyze circular motion
*R8,9*

- only 2 new "big ideas" in circular motion
- 1.1.6. Solving problems with circular motion ideas
*R9,10*- table of ideas and principles needed to solve circular motion problems
*R9* - example showing all the ideas that can impact a circular motion problem
*R10*

- table of ideas and principles needed to solve circular motion problems

- types of situations covered by
- 1.2. PROJECTILE MOTION
*R11-22*- what is meant by
*projectile motion**R11* - 1.2.1. Simple projectile motion
*R11,12*- what is meant by "simple" projectile motion
*R11* - an example using strobe diagram of a ball thrown into the air
*R11,12* - relationship of strobe diagram and plots to Newton's laws and force ideas
*R12* - using plots of v
_{x}and v_{y}vs. time to find a_{x}and a_{y}*R12*

- what is meant by "simple" projectile motion
- 1.2.2. Algebraic representation of simple projectile motion
*R12,13*- using a graph to write an expression for horizontal position vs. time
*R12* - using a graph of velocity vs. time to derive expressions for vertical velocity vs. time and height vs. time
*R12,13*

- using a graph to write an expression for horizontal position vs. time
- 1.2.3. Algebraic representation of two-dimensional motion
*R13*- defining symbols for the vectors
**r**,**v**, and**a***R13* - kinematic expressions for position and velocity as functions of time for constant acceleration
*R13*

- defining symbols for the vectors
- 1.2.4. Free-fall acceleration
*R14*- difference between
*g*and*a*_{g}*R14* - why we use the symbol
*a*to denote free-fall acceleration_{g}*R14*

- difference between
- 1.2.5. Special features of simple projectile motion
*R14*- what is meant by the term
*trajectory**R14* - 3 special features of a trajectory:
*time of flight*,*range*, and*maximum altitude**R14* - labeled diagram of trajectory showing special features
*R14* - what the time of flight depends on
*R14* - what the range depends on
*R14* - what the maximum altitude depends on
*R14*

- what is meant by the term
- 1.2.6. Reasoning about simple projectile motion
*R15-17*- seeing patterns in how the speed and velocity of a projectile change
*R15* - comparing trajectories to understand projectile motion
*R16* - applying Newton's laws to projectile motion
*R17* - applying conservation of energy to projectile motion
*R17*

- seeing patterns in how the speed and velocity of a projectile change
- 1.2.7. Solving problems in simple projectile motion
*R18-20*- 4 relationships needed to solve problems in simple projectile motion
*R18* - 4 keys to solving projectile motion problems
*R18,19*- recognizing that time
*t*is the same in all 4 relationships*R18* - translating given information properly into equation form
*R18* - focusing on special features of trajectories
*R18* - realizing when you have enough equations to solve for the unknown
*R18,19*

- recognizing that time
- 2 examples
*R19,20* - how to interpret a negative root
*R20*

- 4 relationships needed to solve problems in simple projectile motion
- 1.2.8. Solving problems in two-dimensional motion
*R21,22*- 4 relationships needed to solve problems in 2-dimensional motion
*R21* - 2 examples
*R21,22*

- 4 relationships needed to solve problems in 2-dimensional motion

- what is meant by
- 1.3. RELATIVE MOTION
*R23-35*- situations covered by
*relative motion**R23*- some goals of studying relative motion
*R23*

- some goals of studying relative motion
- 1.3.1. Relative motion in one dimension
*R23,24*- 4 people at the airport on or near a moving walkway
*R23* - table of velocities as seen from 2 different perspectives
*R24*

- 4 people at the airport on or near a moving walkway
- 1.3.2. Reference frames
*R24*- what is meant by
*reference frame**R24* - table of positions as measured in 2 different frames at <nobr>
*t*= 0.0 s</nobr>*R24* - why some positions change but other positions stay the same
*R24*

- what is meant by
- 1.3.3. Notation and language
*R25*- labeling frames as "primed" and "unprimed"
*R25* - labeling positions and velocities as "primed" and "unprimed"
*R25* - reasons someone's speed can be zero even though everyone agrees he is moving
*R25*

- labeling frames as "primed" and "unprimed"
- 1.3.4. Relative motion in two dimensions
*R26*- Jamal throws a ball into the air while riding a skateboard
*R26* - to Jamal, motion of the ball is 1-dimensional
*R26* - to Betty, motion of the ball is 2-dimensional
*R26*

- Jamal throws a ball into the air while riding a skateboard
- 1.3.5. Position and velocity transformations
*R26-29*- a boat is crossing a river, while Sue is running along the shore
*R26* - in 2 dimensions, each reference frame has 2 coordinate axes
*R26* - graphical representation of position transformation
*R26,27* - numerical and symbolic representations of position transformation
*R27* - general expressions for transforming positions
*R27* - general expression for transforming velocity
*R27* - 3 representations of velocity transformation
*R27* - general expression for transforming acceleration
*R28* - 2 examples of velocity transformation
*R28,29*

- a boat is crossing a river, while Sue is running along the shore
- 1.3.6. Newton's laws in different reference frames
*R29,30*- science experiments on a train moving with constant velocity relative to the ground
*R29* - laws of physics are the same in a frame moving with constant velocity
*R29* - science experiments on a train slowing down relative to the ground
*R29,30* - Newton's laws and empirical laws are different in an accelerating frame
*R30* - small accelerations have only small effects on Newton's laws
*R30* - definition of the phrase
*inertial frame**R30*

- science experiments on a train moving with constant velocity relative to the ground
- 1.3.7. Conservation of energy in different reference frames
*R30,31*- throwing a ball from the ground and from a moving train
*R30,31* - change in kinetic energy depends on the frame of reference
*R31* - work done by a force depends on the frame of reference
*R31* - table showing how the scenarios look different in different frames
*R31*

- throwing a ball from the ground and from a moving train
- 1.3.8. Reasoning with relative motion ideas
*R32,33*- only 3 new ideas
*R32*- the
**reference frame**is the key to determining positions, velocities, and energy*R32* - when the frames are
**inertial**, forces, masses, and accelerations are the same in all frames*R32* - there is
**no preferred**reference frame*R32*

- the
- sometimes, a situation is easier to analyze in one frame than another
*R32,33*

- only 3 new ideas
- 1.3.9. Solving problems with relative motion ideas
*R33-35*- many common problems involve navigation
*R33,34* - definition of the term
*heading**R35*

- many common problems involve navigation

- situations covered by

- 3 independent sections: circular motion, projectile motion & relative motion
- Chapter 2. Rotational Motion
- situations covered by
*rotational motion**R36* - how we are going to approach rotational motion
*R36* - why we are going to always use a
**fixed**axis*R36* - 3 main sections: angular kinematics, angular dynamics & energy in rotating systems
*R36* - 2.1. ANGULAR KINEMATICS
*R37-42*- what is meant by
*angular kinematics**R37*- why we need to introduce a new set of kinematic quantities
*R37*

- why we need to introduce a new set of kinematic quantities
- 2.1.1. Angular vs. linear kinematics
*R37,38*- description of linear motion
*R37* - description of angular motion
*R37* - what is meant by "CCW" and "CW"
*R37* - CCW rotations are positive
*R37* - table comparing linear motion and rotational motion (fixed axis)
*R38*

- description of linear motion
- 2.1.2. The radian
*R38,39*- why the radian is different from other units of measure
*R38* - why the radian is the preferred unit for angles
*R38* - an example using arc length
*R38,39* - 2 examples applying the radian
*R39* - why certain relationships are not proper
*R39*

- why the radian is different from other units of measure
- 2.1.3. Reasoning with angular kinematics ideas
*R40,41*- angular velocity and linear velocity are very different quantities
*R40* - linear velocity depends on your location on the spinning object
*R41* - the linear velocity can be zero even though the object is spinning
*R41*

- angular velocity and linear velocity are very different quantities
- 2.1.4. Solving problems in angular kinematics
*R41,42*- relationship between angular speed and angular velocity
*R41* - graphs can help organize information and help solve problems
*R42*

- relationship between angular speed and angular velocity

- what is meant by
- 2.2. ANGULAR DYNAMICS
*R43-51*- situations covered by
*angular dynamics**R43* - 2.2.1. Pivots
*R43*- what is meant by
*pivot**R43* - an example using a hinged door
*R43* - why we ignore forces parallel to the axis of rotation
*R43* - what is meant by "about the pivot" or "about the point
*p*"*R43*

- what is meant by
- 2.2.2. Torque
*R44-46*- 4 factors affecting the torque
*R44* - 2 definitions of
*torque*for rotations about a fixed axis*R44* - finding the direction of torque
*R44* - SI unit of torque (N·m)
*R44* - 2 examples
*R45* - definition of
*net torque*for rotations about a fixed axis*R46*

- 4 factors affecting the torque
- 2.2.3. Moment of inertia
*R46,47*- 3 factors affecting the moment of inertia
*R46* - definition of
*moment of inertia*(point mass)*R46* - definition of
*moment of inertia*(composite object)*R46* - 2 examples
*R47*

- 3 factors affecting the moment of inertia
- 2.2.4. Newton's 2nd law in rotational form
*R48*- mathematical description of Newton's 2nd law for rotations about a fixed axis
*R48*

- mathematical description of Newton's 2nd law for rotations about a fixed axis
- 2.2.5. Angular vs. linear dynamics
*R48*- table comparing linear and angular dynamics
*R48*

- table comparing linear and angular dynamics
- 2.2.6. Reasoning with angular dynamics ideas
*R48-50*- for static situations, every axis is a fixed axis of rotation
*R48,49* - 3 examples
*R49,50* - the gravitational force acts "as though" through the
*center of gravity*or*balance point**R49*

- for static situations, every axis is a fixed axis of rotation
- 2.2.7. Solving problems in angular dynamics
*R51*- an example
*R51* - relationship between angular acceleration and linear acceleration
*R51*

- an example

- situations covered by
- 2.3. ENERGY IN ROTATIONAL SYSTEMS
*R52-56*- 2.3.1. Kinetic energy of rotating objects
*R52*- rewriting the kinetic energy using rotational quantities
*R52*

- rewriting the kinetic energy using rotational quantities
- 2.3.2. Potential energy in rotational systems
*R52*- how energy can be stored in a rotational system
*R52* - torque law for a
*torsional spring**R52* - potential energy for a
*torsional spring**R52*

- how energy can be stored in a rotational system
- 2.3.3. Energy for linear vs. rotational motion
*R53*- table comparing energy for linear and rotational motion
*R53* - why we do not refer to "angular energy"
*R53*

- table comparing energy for linear and rotational motion
- 2.3.4. Reasoning with energy ideas in rotational systems
*R53,54*- 2 examples
*R53,54* - importance of using the center of gravity in energy problems
*R54*

- 2 examples
- 2.3.5. Solving problems with energy ideas in rotational systems
*R54-56*- how conservation of energy and the Work-Kinetic Energy Theorem are applied
*R54,55* - why there is no such thing as "angular" energy
*R55* - 2 examples
*R55,56*

- how conservation of energy and the Work-Kinetic Energy Theorem are applied

- 2.3.1. Kinetic energy of rotating objects
- 2.4. SOLVING PROBLEMS IN ROTATIONAL MOTION
*R56*- general guidelines for solving problems in rotational motion
*R56*

- general guidelines for solving problems in rotational motion

- situations covered by

(ISBN 0-7872-5412-6)

*Sorry, but we haven't posted the table of contents for this volume (yet). Contact Bill Leonard for assistance.*

Activities & Reader (ISBN 0-7872-5413-4)

*Sorry, but we haven't posted the table of contents for this volume (yet). Contact Bill Leonard for assistance.*

(ISBN 0-7872-5414-2)

Selected excerpts from the MOP curriculum

Below are links to a few of the "minds-on" activities we have developed, in PDF format. (*Adobe Acrobat Reader or equivalent required.)*

4. Using Graphs of Position vs. Time

11. Translating Graphs of Velocity vs. Time

16. Solving Constant-Velocity Problems Using Different Methods

46. Comparing Magnitudes of Common Forces

50. Recognizing and Interpreting Free-Body Diagrams

59. Reasoning With Newton's Laws

77. Reasoning with Impulse and Momentum Ideas

86. Recognizing and Comparing Kinetic Energy

91. Computing the Potential Energy

101. Solving More Complex Problems

FF·1. Exploring Models of Electromagnetism

FF·5. Exploring the Magnetic Interaction

FF·9. Exploring the Gravitational Interaction

FF·11. Distinguishing Mass and Weight

FF·13. Using a Mathematical Model for the Electric Force

FF·20. Reasoning with Universal Gravitation

FF·25. Representing Vector Fields Using Field Line Diagrams

FF·27. Applying Work and Energy Ideas

AT·1. Exploring Ideas About Circular Motion

AT·5. Reasoning About Circular Motion

AT·9. Reasoning About Projectile Motion

AT·14. Reasoning About Relative Motion

AT·16. Graphing Rotational Motion

AT·17. Introducing Rotational Kinematics

AT·20. Solving Rotational Dynamics Problems

AT·21. Identifying Energy in Rotational Systems

*Nothing available here (yet??)...*

An excerpt from the MOP teacher's guides about how to use MOP effectively

This section describes how to get started with MOP. Ideally a teacher would work through all of the student activities and read through all of the accompanying materials in the MOP *Teacher's Guides*. Only then can a teacher make well-informed decisions about how to best use the MOP materials to meet their instructional needs and goals. Our experience, however, is that this ideal is unrealistic for most teachers. Teachers have little disposable time they can devote to mastering a new curriculum, and so, teachers must "learn as they go." It can take teachers as long as three years to become thoroughly comfortable and familiar with a new curriculum. We hope the contents of this section will help make getting started with MOP as efficient and effective as possible.

*Getting Started* covers the following areas:

- MOP Curriculum Materials
- Components of a MOP Activity
- About the MOP Reader
- Contents of the Teacher Aids
- A Note on Laboratories, Demonstrations, and Hands-On Activities
- Global Issues: Planning the School Year with MOP
- Creating a Lesson Plan Around a MOP Activity
- Formative and Summative Assessment with MOP

To get the most out of this section, it is best to have your copy of the MOP materials handy and refer to it as needed. MOP Curriculum Materials

There are two sets of materials with MOP, a set of four booklets for students and a corresponding set of booklets for teachers. The first three booklets deal with topics in mechanics: *Motion*, *Interactions*, and *Conservation Laws & Concept-Based Problem Solving*. The fourth booklet --- *Fields, Complex Systems & Other Advanced Topics* --- applies the principles developed in the first three booklets to a wide range of physical phenomena.

Each student booklet is divided into two parts: The *Activities* form an integrated set of thoughtful engagements for students, and the *Reader* organizes and summarizes the ideas of the physics content and is meant to be read after students have engaged in associated activities.

Each corresponding *Teacher's Guide* also has two parts: Answers and Instructional Aids for Teachers, which provides advice for how to optimize the effectiveness of the activities, as well as brief explanations and comments on each question in the student activities, and Answer Sheets, which may be duplicated and distributed to students as desired. Use of the answer sheets is particularly recommended for activities requiring a lot of graphing or drawing.

The first booklet in the teacher series contains three supplements:

*Supplement A: Collaborative Group Techniques*provides a short list of ideas for structuring in-class group activities.*Supplement B: Concept-Based Problem Solving*gives a more detailed account of the MOP approach.*Supplement C: A Comparison of the Minds•On Physics Approach with the NRC's National Science Education Standards*presents a list of the core standards contained in the published 1996 National Research Council Science Education Standards and a brief description of how MOP addresses each standard.

The MOP activities all have the same basic structure:

*Purpose and Expected Outcome.*In this section, we tell students the specific concepts, principles, and other ideas that will be raised and addressed during the activity. This section also tells students what they are expected to learn.*Prior Experience / Knowledge Needed.*We first list for students the concepts and principles they should know or be familiar with before attempting the activity. Then, if necessary, we provide any additional background needed to do the activity.*Main Activity.*This section contains the specific questions and problems that probe students' understanding and prepare them to make sense out of the ideas.*Reflection.*After finishing the Main Activity, students re-examine their answers to look for patterns. They are also asked to generalize, abstract, and relate concepts to the situations they have studied.

Occasionally an activity will contain an additional component:

*Integration of Ideas.*This section is used to get students to bring together different but related ideas --- often dealt with using separate situations in the activity --- to analyze a single, often more complex, situation.

Although a MOP activity has several components, the Main Activity and Reflection are the most important. We recommend getting students to the Main Activity as quickly as possible and not overdoing the preparation of students. Students may struggle, but most of their difficulties can be addressed as they proceed through the activity. Students may feel frustrated initially, but with some reassurance from the teacher and a little experience facing and overcoming the inevitable confusion associated with starting something new, students will grow into confident and independent learners.

Nevertheless, it is worthwhile helping students become aware of the structure of the MOP activities. This can be done gradually and indirectly by *meta-communicating* with students. For example, on occasion ask students if they learned what they were expected to learn --- and how do they know. Sometimes have students consider whether they have the knowledge needed to do the upcoming activity. Test their knowledge by asking them some basic questions. Another good idea is to check whether students understood the directions given in the Main Activity. This can be accomplished by stopping the class (after students have had a reasonable chance to get started) and asking individual students or groups of students to share with the class how they are approaching the activity. Ask the class whether the approach meets all the requirements set forth in the directions. After students finish an activity ask students to tell you what is the purpose of the activity from their perspective.

There is no traditional textbook with MOP. There is a Reader, but it serves mostly as a follow-up to the MOP activities. The intent is that students begin by working the activities with little or no preparation from the teacher or from any other source material. Any preparation that might be needed is provided in the *Prior Experience / Knowledge Needed* sections of the activities. The appropriate part of the Reader is designed to be read after the student finishes the corresponding activity (or set of activities), and is intended to summarize, organize and integrate the ideas and issues raised in the activities. The students can then use the Reader as a resource for later activities. Guidance for reading assignments is provided in the Instructional Aids. Contents of the Teacher Aids

The *Answers and Instructional Aids for Teachers* are our way of communicating the philosophy behind each activity and/or set of activities. We explain our goals and our expectations for each activity, and try to give warnings about student difficulties, misunderstandings, and common responses. We also suggest ways to interpret different patterns of students' responses as well as ways to assess student understanding. The Instructional Aids are intended to prepare teachers in their role as coaches of students' learning.

*Answers with Short Explanations*--- Answers are an invaluable resource. At the very least, they allow teachers to see how we think about a situation or problem. A short explanation or remark is always provided with an answer. Our intent is to emphasize the process of analyzing each question, being aware of one's assumptions, and arriving at an answer consistent with those assumptions. When appropriate we indicate how the question might be answered differently under different assumptions. Frequently we also indicate how students might answer the question or how they might reason about the situation. Although we provide answers, we wish to stress that the focus should always be on students' thinking process and never exclusively on whether an answer is right or wrong.*Goals and Objectives*--- Identifies the physics concepts that will be dealt with in the activity and gives a brief statement of the expected outcomes.*Time Needed for Activity*--- Provides an estimate of the time needed to complete the activity. Since there are a number of ways to approach each activity this estimate is very rough. Other factors, such as class ability or path through the material, will affect the time required for an activity. We suggest for future reference that you keep a log of the actual time needed.*Preparation for Students*--- Identifies what students need to know before they begin the activity. Typically only two or three major items are mentioned per activity. Our intent here is to assure that the majority of the students have been prepared to a certain threshold. Clearly knowledge is cumulative and gaps in students' knowledge/skills are inevitable. Only the teacher can gauge whether or not the class as a whole is ready for an activity. Our advice is not to be unduly timid about moving ahead. However, be prepared to provide students the support they need.*Link to the Reader*--- Indicates which sections of the Reader the students may read after finishing the activity. Students will often be asked to do several activities in succession with no reading assignment.*Suggestions for Classroom Use, Organization, etc.*--- Contains a variety of information particularly relevant to creating a lesson plan for the activity. Suggestions are made regarding which parts of the activity to do in class and which parts to do for homework. Sometimes there are suggestions for introducing the activity. There are also suggestions on which parts students might do alone, which parts they might do in groups, and which parts might be done as a class. There are also suggestions for incorporating hands-on materials into the activity.*Anticipated Difficulties for Students*--- Informs teachers about difficulties students are likely to have with the activity. We list only a few items --- ones we think many students will share. There are, of course, many more student difficulties that we do not list, and some of these might actually be more common than the ones we have listed. It is useful to keep a log of the most prevalent ones.*Probing for Student Understanding*--- Contains a list of questions that can be used to assess student understanding. The questions can be used to gauge student progress on the activity as well as to identify areas of concern. Many of the items could also be used as exam questions.*Suggested Points for Class Discussion*--- Raises some important points for discussion. A class-wide discussion provides a wonderful opportunity for students to hear views of others and get feedback on their own points of view.*Providing Support to Ensure Student Progress*--- Provides some interventions that teachers can try when students get stuck.

The MOP approach stresses the value of building the physical representation for physics concepts and principles, and integrating this with more formal representations. Consequently, some of the activities involve extensive use of hands-on activities. Clearly, laboratory exercises and demonstrations also serve to develop the physical representation and a good course will employ these methods as well. We wish here to argue that simple, unstructured explorations of physical ideas in a qualitative, hands-on manner serves an important function not met by typical demonstrations and formal laboratories.

Traditional formal labs tend to be cook-book in nature, to involve large amounts of data manipulation and analysis, and frequently culminate in time-consuming lab reports. They are often unmotivated from the students' point of view and do not seem to impact learning of physics. To be sure, there are a multitude of skills to be learned from good laboratory experiences, but command of the physical representation is not a common result. Many excellent laboratory materials have already been published and we have elected not to duplicate that effort. In our experience most teachers have strong preferences for the laboratory exercises that they use and just about any laboratory is compatible with MOP.

In many classrooms, demonstrations are used to exemplify a particular concept or principle, with the interpretation, description and explanation provided by the teacher. For a thinking student, however, a demonstration often raises many more questions than it answers, and without the opportunity to investigate those questions, students can come away with very distorted views about what the demonstration means. To become convinced of this, ask your students what they think they have observed after a demonstration **before you tell them what they should have observed**. We recommend a broader use of demonstrations as a means for students to explore the features relevant for understanding physical systems and the reasoning used to analyze them. To maximize the effectiveness of demonstrations, we encourage teachers to use a reason-predict-show-explain sequence of activities, in which students think about the demonstration apparatus, predict what they believe will happen, observe the demonstration, and then describe the reasoning behind their predictions. (This is sometimes called an

In our view, simple commonplace manipulatives, such as balls, marbles, springs, strings, and toy trucks, should be well integrated into the course. Students should have continuous access to these materials, and they should be frequently asked to employ them to demonstrate physical ideas and principles in a qualitative manner. This is a very difficult task for students. Perhaps the only thing more difficult for students than translating their ideas into physical reality is explaining what they are trying to accomplish to another person. For this reason small group or class discussions of hands-on activities are particularly fruitful for interrelating the linguistic, formal, and physical representations. Global Issues: Planning the School Year with MOP

How you implement MOP during your school year depends strongly upon your instructional objectives for your specific class. There are many possible objectives, ranging from preparing students for college science courses to exposing students to the broadest possible range of physics phenomena. Faced with a particular class, many teachers feel that these two objectives are in conflict and they must strike some compromise. Indeed, because time is limited, every teacher is constantly making choices regarding how to spend their class time.

We would argue that your most important objective is to make your students self-aware and self-motivated learners, and that MOP can help you accomplish this. Many students are intimidated by physics, feel inadequate to do physics and, consequently, disengage. Students spend far too much time looking for the right answer or, even worse, the answer they think you want. Discussing these issues and your expectations openly will help them focus on the only meaningful outcome, their own learning and development. Obviously, it is important to reward engagement and effort. Such rewards, however, should not confuse students by creating the impression that all reasoning is equivalent and just a matter of taste.

Touching upon many topics and modern phenomena is a desirable goal. Such exposure, however, is only effective and long lasting if students have some firm ground of fundamental concepts to which they can relate this knowledge. Building a solid foundation is what MOP is all about. Depending upon individual goals, the mechanics portion of MOP (i.e., the first three booklets) should occupy between 1/2 to 3/4 of the school year.

Although the MOP activities are numbered, there is no need to proceed through them in strict order. Nor is there a need to do every activity or any particular activity in its entirety. While there is no single best path through the materials, it is best not to invert related activities designed to target different cognitive stages. As mentioned in the *Letter from the Authors* and as elaborated in *Supplement B: Concept-Based Problem Solving*, MOP activities dealing with the same topic are sequenced in a cognitive sense. Students are encouraged to (a) explore their current understanding, (b) refine and interrelate their physics concepts, (c) enhance their analyzing and reasoning abilities, (d) develop problem-solving skills, and (e) organize their knowledge into a coherent structure.

Which activities should be used and how much time should be devoted to each of them is something only you can decide. The activities are intended to be a resource, not a recipe. We offer the following general advice for your consideration:

- Emphasize the need for good communication between students and yourself and among the class as a whole. Students who understand what is being asked of them are usually much more successful. It should be explained to students that it is not the answer alone that is important, but the relationship between their reasoning and their answer.
- Do not let students get bogged down. Even the best of students may not get the desired idea on the first pass. It often takes students considerable time to accommodate and learn how to use new ideas. Rather than wait for all students to demonstrate the proficiency with a specific concept that you would like, move on, but with the intention of returning to the topic at a later time.
- Keep course topics integrated with each other. Students often perceive an introductory physics course as a series of unrelated topics. Rarely do teachers ask students to find the velocity or position of a body once kinematics is over and Newton's laws are being covered. Sometimes this tendency to partition is even more common with mathematical topics such as graphs and vectors. Many teachers use graphs extensively while covering kinematics and never use them again. Create opportunities for students to interrelate their knowledge and skills. A spiral, multi-pass approach is more effective for learning and structuring knowledge than a one-pass approach.
- As a special case of the above points, consider interweaving motion with interactions. The topics of kinematics (vectors, algebra, graphs, rates of change, etc.) are among the most difficult for beginning students. There is no need to wait for this formal math development to finish before beginning to develop physical intuition and reasoning skills. The two can be developed in parallel. This has the added advantage of keeping students more interested and motivated because most students consider kinematics a resounding bore. On the other hand, when they see why one might be concerned about the velocity and position of an object subject to a net force, they are more motivated to learn kinematics.

Once you decide to use a MOP activity:

- If possible, invest the time to do the activity yourself. This is the best way to become familiar with the activity, and you will be in a better position to make decisions. Read over the instructional aids to get a general sense of the issues being addressed in the activity.
- Choose the hands-on materials that will be available.
- Decide how to introduce the activity. Should you let students just jump in, or should you ask a probing question beforehand, or should you do an interactive demonstration? For instance, you might discuss the Goals and Objectives with your class, or work on the example, or even do part of the activity as a class exercise.
- Select the portions of the activity you want to do, which parts will be done in class and which parts might be done for homework.
- Decide how students will engage in the activity. Should it be done as a class, in groups, in pairs, or individually? When should the class discussion begin? Should students present their answers to the rest of the class and, if so, how?
- Think about ways you can support students' progress through the activity.
- Select points for class discussion and/or question(s) to probe student understanding.
- Look at the explanations and comments provided with the answers to get some sense of how students might respond to the various questions and what these responses might mean.

Most assessments used by teachers are at the end of a topic and are of a *summative* nature, that is, they serve to evaluate student progress and assign a grade. Only rarely are tests designed to inform either students or teachers of the nature of student difficulties. Assessments of this second type are called *formative* because the results have consequences for subsequent instruction. Generally, it is preferred to identify student problems or misunderstandings while there is still time to do something to correct the situation. The MOP approach emphasizes the need for formative, as opposed to summative, assessment.

We know that the traditional ways of testing students do little to uncover conceptual difficulties or to measure knowledge of physical laws and principles. Traditional exam questions tend to stress answers and be numeric and formulaic in nature. New ways of assessing students' progress must necessarily be developed alongside new approaches to teaching. These new assessments need to encourage students to focus on those features that are important for deep understanding. Without new assessment methods, students will remain largely unwilling to abandon formulaic approaches. Examples of how new assessments might be structured to probe students' progress and their conceptual understanding can be found in the "Probing for Student Understanding" sections of the *Answers and Instructional Aids for Teachers*. Another suggestion is to reserve part of an activity for a later assessment. If students are to demonstrate their abilities, it is important that the assessment item resemble the tasks that they have rehearsed.

Finally, it is our view that tests and exams should serve primarily a pedagogic rather than evaluative function. Students dislike and resent exams because they feel evaluated, i.e. their worth is determined. Failure erodes their self-confidence and self-esteem. Success on traditional exams does not send a much better message. Successful students come to believe that achievement in the form of grades, rather than intellectual development, is the goal to be sought. Exams can be designed to be informative to students and can serve as valuable educational experiences for students. Students need to go beyond being active, or even engaged learners. They need to become self-invested in the entire process of education. They need to develop self-evaluation skills and good exams can help them achieve this goal. Frequently asking students to what they attribute their lack of success or inability to do a problem helps them establish self-reflection as the norm. Teaching self-invested and reflective students is an exciting and rewarding experience.

*Minds•On Physics* is sold by the Kendall/Hunt Publishing Company.

If you are a teacher using Minds*On Physics...

Are you a teacher who uses Minds•On Physics? If so, we'd love to hear from you. Please don't hesitate to contact Bill Leonard with any questions, comments, or feedback.

You should probably check out the MOP Errata page, too.

Corrections for errors (gasp!) in the published MOP books

Believe it or not, we have errata lists for the following books. ("TG" means "Teacher's Guide" and "AR" means "Activities & Reader", i.e., the student activities book.) If you think you've found a mistake that we don't list here, please report it to Bill Leonard.

We'll add errata pages for the other books if/as the need arises.

Student Reader, p. R4, middle:

- The components of the position of the ant should be given everywhere in "centimeters"
**not**"meters". [EH, 06Jun04]

Student Reader, p. R9, top:

- The average velocity from
*t*= 5.0s to*t*= 6.0s is +10cm/s,**not**−10cm/s. [AW, 14Jan04]

*Many thanks to Andrew Wertz of Littlestown HS in Littlestown, PA, and Ed Haley of E.C.O.S. in Springfield, MA, who found these mistakes.*

Activity 4, p. 22, question P8, part (a) answer

- Add graph D to the list of answers, i.e., "Graphs
**C, D, and E**represent objects that are speeding up."

Activity 8, p. 39, "Link to Reader"

- Change the ending page of the reading assignment to R9, i.e., "Students may read pages R8-9 (the beginning of section 1.4, Velocity)
**after**finishing Activity 9."

Activity 9, p. 45, "Link to Reader"

- Change the ending page of the reading assignment to R9, i.e., "Students may read pages
**R8-9**(the beginning of section 1.4, Velocity)**after**finishing this activity."

Activity 9, p. 46, "Probing for Student Understanding", question P3

- In parts (a) and (c), change the units to cm/s, i.e., "
**P3.**(a) Which object (in part A) reaches a**velocity**of 1cm/s first? (b) When does this occur? (c) Which object reaches a**speed**of 1cm/s first? (d) When does this occur?"

Activity 12, p. 65, question A4 answer, bullet 1

- Change wording to "Students might plot speed vs. time instead of velocity vs. time (as shown below on the left). In addition, some students might not realize that the speed goes to zero between strobes 4 and 5 (as shown below on the right)."

Activity 12, p. 68, question B4 answer

- Change answer to "
**after**".*t*= 0.45s - Add third bullet, "• By exaggerating the curvature of the graph between #4 and #5, you can see that the marble is at the 1m mark just after the midpoint in time."

Activity 13, p. 76, question P1 answer

- In part (a), at
*t*= 1½s, object X is at*x*=**7½cm**.

Activity 14, p. 79

- question A2 answer, bullet 1, "Object J has the largest displacement..."
- question A4 answer, bullet 1, "Students might pick only object J, because object I..."
- question A4 answer, bullet 2, "Students might pick only object I..."
- question A6 answer, "... which would correspond to
**J**" - question A6 answer, bullet 1, "Students might pick object I because the curves for objects E and I look the same."

Activity 15, p. 86, question P1 answer

- The answers to parts (a) and (b) are reversed.

Activity 16, p. 91, question C3 answer

- Modify paragraph 2: "
**Yes**, this answer agrees..." - Fix bullet 1: "Students might have gotten question B2 wrong."

Activity 17, p. 96, question A5 answer

- Add to the end of paragraph 1, "At 20km/h, the plane travels
**about 5½km**before losing contact with the car." - Add to the end of bullet 1, "i.e., after the plane has traveled 20km".

Activity 19, p. 107, question P4 answer

- The speed is only 1 grid/s, i.e., the answer should read, "... the average velocity is
**+1 grid/s**—or— **1 grid/s, to the right**between 2s and 6s."

Activity 23, p. 131, question P8 answer

- Add bullet, "• See table of values for P1 above."

Activity 24, p. 137, question B1 answer, bullet 4

- Change A2-A4 to B2-B4, i.e., "Students do not need to make precise calculations to answer questions B2-B4."

Activity 25, p. 145, question A2 answer

- In part (i), the Total Area (i.e., column 4) should be 292.5 m.

Activity 27, p. 163

question R2 answer is really only the first half of the answer to R2.

question R3 answer is really the second half of the answer to R2.

question R4 answer is really the answer to R3.

question R5 answer is really the answer to R4.

*Many thanks to Lonnie Grimes of Oakmont High School in Roseville, CA, who found almost all of these mistakes.*

Activity 37, p. 146, "Explanation of Activity and Examples":

- The page number indicating where to find the map (of King's Court) should be "143",
**not**134.

*Many thanks to Patrick Diehl of Ashley Hall School in Charleston, SC, who found this mistake.*

Activity 36, p. 216, question A4 answer

- Quadrant (column 1) should be "2 only", angle relative to horizontal (column 2) should be "27°", and angle relative to East axis (column 3) should be "153°".

Activity 36, p. 217

- Answer to question B2 should be:
**580m @ 149°**. - Answer to question B3 should be:
**500m @ 307°**. - Answer to question B3, bullet 1: replace -37° with -53°.

Activity 37, p.222, "Suggested Points for Class Discussion", bullet 2

- The word 'needs' should be 'need', i.e., "... both the origin and the orientation of the coordinate frame need to be specified..."

Activity 38, p. 227, question A5 answer

- All the answers for vector
**V**are wrong. There should be a minus sign in front of each term, and the length of the vector is 4.24cm. So, the*x*-component of**V**can be written either -(4.24cm) cos(45°) or -(4.24cm) sin(45°), and the*y*-component of**V**can be written either -(4.24cm) sin(45°) or -(4.24cm) cos(45°).

Activity 38, p. 229, question B5 answer, bullet 2

- Change B3 to B2, i.e., "Students might use a rotated coordinate system (as in B2)."

Activity 42, p. 258, question B1 answer, bullet 1

- Rephrase third sentence to read, "This is the only situation in this part for which buoyancy is considered relevant."

Activity 44, p. 267, "Probing for Student Understanding"

- Change part (b) of question P3 to read, "In part B, how would the readings on scales A, B, and D change if scale C were removed?"

Activity 45, p. 280

- In the answer to question I7, add object E to the list, i.e., "
**Only objects A, B, D, and E****must**have friction forces exerted on them." - The answer to question R3 is missing. It should read, "The objects considered in situations A3, A6, and B3 could be accelerating. For the rest, the object has a constant velocity.
- There are no comments for R3. They are,
- "Students might not include A3, perhaps because they think the ball is not accelerating at the top of its trajectory."
- "Students might include B1, perhaps because the book is accelerating. But the object being considered is the table, which is not accelerating."
- "Students might not include B3, perhaps because they think that the ball is at rest when it is touching the wall."
- "At this point in the course, students are not expected to know the relationship between force and acceleration. Students should be encouraged to determine which objects definitely have no acceleration. The rest can be considered to possibly be accelerating."
- The answer for question R4 is missing. It should read, "(Students indicate any forces other than the seven introduced here that they have heard of. They then indicate if any of these other forces behave like any of the forces introduced here."

Activity 45, p. 281

- The answer to question P5 is wrong. It should read, "If the spring was compressed rather than stretched, then
**the strings would be angled inward, rather than outward**. In other words, object G would be hanging to the left of where its string is attached to C, and object H would be hanging to the right of where its string is attached to C." - The comment for the answer to question P5 does not fit any longer. It should read, "Students might not think it is possible for the spring to remain compressed between objects G and H."

Activity 46, p. 284, "(More Ways of) Probing for Student Understanding"

- Question P6 is question P4.
- Question P7 is question P5.
- Question P8 is question P6.

Activity 47, p. 294, question R2 answer

- Change 'part B' to 'part A', i.e., "In situation C of part A, the normal force..."

Activity 48, p. 297, "Suggested Points for Class Discussion", bullet 2, last sentence

- The word 'a' should be 'at', i.e., "(Thus, one can be at rest; the friction is still kinetic.)"

Activity 49, p. 307

- The first entry in the table is not the beginning of the answer to question A4, but a continuation of the answer to question A3.
- The answer to question A4 begins with gravitation.
- There is a force missing from the answer to question A4. The force (i.e., column 1) is "kinetic friction." The way it will be determined (column 2) is "Multiply the normal force by the coefficient of kinetic friction. Direction is opposite the motion of _m_
_{1}." The magnitude & direction (column 3) is "(NA)." Comment is "• We do not actually**know**the normal force, so we cannot determine the force of kinetic friction. However, students might think that they know the normal force using common sense."

Activity 49, p. 308, question R1 answer

- The second bullet for air resistance is wrong. It should read, "At
**very small**speeds, the force law is closer to*Bv*.

Activity 51, p. 324

- The answer to question B1, part (a) is wrong. The
*x*-component of**F**_{_N_,left}should be*F_*,left._{_N} - The answer to question B1, part (b) is wrong. The
*x*-component of**F**_{_N_,right}should be -*F_*,right._{_N} - The answer to question B2, part (c) is confusing. Vectors
**F**_{_g_1},**F**_{_N_2}, and**F**_{_T_2}are not part of the answer. They are simply the other vectors in the situation, which are included because their components are known. - The answer to question B2, part (d) is wrong. The
*x*-component of**F**_{_g_2}should be -*F_*-component should be -_F__{_g_2}cos 60°, and its _y_{_g_2}sin 60°. - The word "the" should be removed from the second line of the last bullet for the answer to question B2, i.e., "Even if we notate the magnitude of both tension forces as..."

Activity 54, p. 350, question P9 answer

- Change "velocity" to "velocities", i.e., "(a,b) The forces...
**Kinetic Friction**, which depends on the relative velocities of the objects in contact, and..."

Activity 55, p. 357, question A5 answer

- In the table showing the time intervals during which the ball is accelerating, change '4.9s' to '4.8s', i.e., the time interval corresponding to the 2nd time the ball is rolling across the felt should be [4.8s, 6.5s].
- In the table showing time intervals during which its velocity is constant (it's part of the 4th bullet of the answer to question A5), change '4.9s' to '4.8s', i.e., the third time interval during which the ball is rolling at constant velocity is [3.51s, 4.8s].

Activity 56, p. 370, question C4 answer, bullet 3

- Change 'any' to 'a', i.e., "Students might not perceive that there is a net force on them when they walk in a circle."

Activity 58, p. 384, question A2, part (c) answer

- Of the three free-body diagrams, the one on the left is for the skydiver, the one in the middle is for the parachute, and the one on the right is for the Earth.

Activity 58, p. 386, question B4 answer

- Add to the end of the answer to part (b): "But perhaps not as much faster and farther as before, assuming for example that she does not push as hard as her father did before."
- Add a bullet: "• In other words, her speed might be smaller than it was before, but it is always larger than her father's."

Activity 58, p. 387, question R1 answer, bullet 1

- Change to "The action-reaction pair has
**five**features: exerted**by**different objects, exerted**on**different objects, same type (normal, gravitational, etc.), same magnitude, and opposite direction."

Activity 59, p. 389, "Suggestions for Classroom Use"

- Change bullet 2 to: "Focus students' attention on learning the answers and explanations to two questions using the following group structure: Divide the class into teams of 3 or 4 students each. Assign each team 2 questions from the same part, or put slips of paper with the numbers of 2 questions into a bowl and have teams choose. Tell students that each of them will be asked to write out the explanation to one of the questions, and that each student's grade will depend in part on how well the other team members do. As the teams are working, decide which explanation each student will provide. When the working time is complete, give students their assignments, to be done either during or after class. When grading explanations, give half credit for each individual's contribution and half credit for the contributions of the rest of the team. In other words, half of each student's grade will depend on his/her individual explanation, and the other half will depend on his/her team's explanations.
- Insert between bullets 2 and 3: "• For small classes with only a few teams, do parts B and D first, then repeat with parts C and E."
- Add bullet: "• As a class, compare answers and discuss areas of disagreement."

Activity 59, p. 391, question A4 answer

- Change 'rope 1' to 'rope 2', i.e., "... then the tension in rope 2 is larger in case II than in case I."

Activity 59, p. 392, question C2 answer

- Add bullet: "• Students might think that the velocity is larger because the net force is larger."

Activity 60, p. 402, question R2, part (a) answer

- Remove 'of the', i.e., "The mass
**is much larger for the car**."

*Many thanks to Lonnie Grimes of Oakmont High School in Roseville, CA, who found almost all of these mistakes.*

Activity 74, p. 513, question B3, part (c) answer

- In the second paragraph, the area of each 'box' is wrong. It should be 0.01N-s, i.e., "... and each box has an area of (2N) x (0.005s) = 0.01N-s..."

Activity 76, p. 529, question A3 answer

- The parts are not labeled, i.e., the "(a)", "(b)", and "(c)" labels are missing.

Activity 76, p. 532

- The answers and comments to questions R1, R2, and R3 are missing.
- The answer for R1 is, "Total momentum is conserved for situations A3 and A6. It is zero initially, and remains the same throughout the time interval specified. Total momentum is
**approximately**conserved for situation A1, because the impulse delivered to the system by gravitation is small during the explosion. At least one component of the total momentum is conserved for the other 5 situations. We define the*x*-direction to be the horizontal in the plane of the page (i.e., to the right), the*y*-direction to be the vertical, and the*z*-direction to be the horizontal perpendicular to the plane of the page (i.e., directly toward you). In situations A2, A4, and A7, the net external force is in the*y*-direction, so total momentum is conserved in the*x*- and*z*-directions. In situation A5, the net external force has*y*- and*z*-components, so momentum is conserved only in the*x*-direction." - The comments for R1 are:
- Students might think that momentum is not conserved in situation A6, because the wheel is slowing down.
- Students might consider only the ball in A3, rather than the Earth-ball system.
- In situation A3, students might not ignore the gravitational forces exerted on the Earth-ball system by the Sun, the Moon, and the planets.
- Students might not recognize that the total momentum of the Earth-ball system is staying the same during the motion of the ball.
- Students might only consider two directions, i.e., the
*x*- and*y*-directions. - In situation A5, we are assuming that the bow string exerts a force on the arrow in the
*yz*-plane. - Students might think that momentum is not conserved in any direction in situation A7, because the ball's are going in all directions.

- The answer for R2 is, "In situations A3 and A6, all forces are internal; the net force on each system is zero."
- The comments for R2 are:
- If students do not have the correct set of situations here, they are likely to generalize improperly.
- Students might not realize that in A3 they are expected to ignore the forces exerted by the Sun, the Moon, and the other planets.
- Students might not realize that in A6 the net force on the wheel is zero, because it is slowing down.

- The answer to R3 is, "For those situations in which momentum is not conserved, there are external forces on the specified system. In each case, the direction of the change in momentum is the same as the direction of the net external force. In order to always conserve momentum, it is necessary to choose a system large enough so that there are no external forces on it. If we include the Earth in each system and ignore the gravitational forces exerted by the Sun, the Moon, and the planets, then momentum is conserved in all the situations."
- (There are no comments for R3 at this time.)

Activity 83, p. 584, question A1 answer

- The explanation (column 5) should read, "Monkey exerts
*F_*. Whatever is holding up the rope exerts _F__{_N_1}and _F_{fs}_{_N_2}(assuming, e.g., that the rope is tied to a hook in the ceiling). The displacement of the rope is zero."

Activity 87, p. 616, "Anticipated Difficulties for Students", bullet 7 (i.e., last bullet)

- The 'clay' should be a 'cart', i.e., "Analyzing the cart in situation R3... because the work done on the cart is done..."

Activity 87, p. 618, "Providing Support to Ensure Student Progress", bullet 6 (i.e., next to last bullet)

- Change to: "In situation R3, focus students attention on forces that are applied through a displacement, such as forces internal to the spring, rather than forces that are applied through zero displacement, such as the normal force exerted by the wall."

Activity 87, p. 620, question A3(b) answer

- The explanation is wrong, because we do not know how to calculate the work done by friction, as described in the Reader. Therefore, students are expected simply to use common sense to try to answer this question. Later, the explanation will be that there is a loss of energy from the macroscopic realm to the microscopic realm, which means that the speed must be
**smaller**after hitting the spring than before.

Activity 87, p. 620, question A3(b) bullet

- The comment is inappropriate for the same reason that the explanation is inappropriate, that is we do not know how to calculate the work done by friction, as described in the Reader. It should read, "The work done by the friction force on the cart cannot be calculated or even estimated. Further, knowing its value would be of no consequence here, because all of the
**macroscopic**kinetic energy lost by the cart becomes**microscopic**energy of the cart. In other words, the forces are internal to the cart, so the energy remains with the cart. However, at this point in the course, students are not expected to be able to make this distinction between macroscopic and microscopic energy."

*Many thanks to Lonnie Grimes of Oakmont High School in Roseville, CA, who found almost all of these mistakes.*

The following mistakes are in the first 3 printings of Vol. 4·AT / Activities & Reader. If you have a 4th printing or higher, they have been fixed. Please check the copyright page (page iv) to see which printing, or mixture of printings, you have.

Contents, p. v

- The correct title of Activity AT·13 is "Exploring Relative Motion in One and Two Dimensions".

Activity AT·4, p. 13, "Prior Experience/Knowledge Needed"

- The label of the first equation should read:
**tangential component of acceleration**. The change in speed can be negative, and when it is, the direction of the tangential component of acceleration is opposite the direction of motion. And when the change of speed is positive, this component is in the direction of motion.

Activity AT·8, p. 30, question A3

- In the description of the situation, the speed of the marble three seconds later should be "80cm/s",
**not**"79cm/s".

Activity AT·8, p. 31, question B2

- In the description of the situation, the second sentence should begin: "One second later..."

Activity AT·8, p. 31, question B3

- In the description of the situation, the time at which the toy car stops near the top of the incline should be "
*t*= 0.58s",**not**"*t*= 1.8s". - The fourth question in part (d) should be: What is the car's position and velocity at "
*t*= 0.68s",**not**"*t*= 2s".

Activity AT·11, p. 44, question A1

- In the description of the situation, the initial speed of the puck should be "250cm/s",
**not**"25cm/s".

Activity AT·17, p. 69, questions B1 & B2

- A car traveling at 29m/s is moving at "65mi/h",
**not**"60mi/h". This mistake occurs twice in question B1 and once in question B2.

Activity AT·17, p. 69, question B3

- The diagram of situation A is not consistent with what is happening. In particular, there is not enough string left hanging to allow the wheel to spin as many times as it needs before stopping. The following diagram replaces the one accompanying the description. Right-click or command-click and choose “Open image in new window” (or equivalent) to see a full-sized version. Print that version at 100% for a transparency, or at 33% to replace the figure in students’ books. Also note that the diagram on the answer sheet is the Teacher's Guide is the same as that shown below. Finally, the angle of the incline in situation B has been made more shallow to be consistent with the additional changes listed below.
- Many of the values for the given information should be changed. The initial speed of the wheel is now
**1rev/s**, and it is slowing down at a rate of**¼rev/s**. The ball is now a^{2}**marble**, and it is rolling up the incline at**4m/s**and slowing down at a rate of**1m/s**. (Changes shown in^{2}**bold**type.) - The question for part (b) should read: "Write an expression for the position of the
**marble**..." (Change shown in**bold**type.)

Activity AT·18, p. 73, question A5

- In part (b), when the car speeds up, its speed in miles per hour should be "65mi/h",
**not**"60mi/h". In other words, 29m/s = 65mi/h.

Activity AT·21, p. 86, question R4

- The "second" part (b) should be part (c).
- Part (c) should be part (d).

The following mistakes are in the first printing of Vol. 4•CS / Activities & Reader. If you have a 2nd printing or higher, they have been fixed. Please check the copyright page (page iv) to see which printing, or mixture of printings, you have.

Activity CS•3, p. 13, question A2(c)

- The mass of oil (fluid X) should be "16" (grams),
**not**"18".

Activity CS•11, p. 50, property #4 of idealized fluids (at the very bottom of the page)

- The middle of the sentence should read: "... which means that both the pressure and speed are constant...".

Activity CS•11, p. 51, "Explanation of Activity"

- The mass of 10cm
^{3}of oil should be "8g",**not**"9g".

Activity CS•11, p. 51, figure for problem A3

- The following figure should make it clearer to students what is going on here, i.e., the direction in which the glass tube is rotated so that it "rests on its side" in part (a). Right-click or command-click and choose "Open image in new window" (or equivalent) to see a full-sized version. Print that version at 100% for a transparency, or at 33% to replace the figure in students' books. (The answer sheet in the Complex Systems TG already has the corrected figure.)

Activity CS•12, p. 53, "Purpose and Expected Outcome"

- The last sentence should begin: "When you find a system
**to which**you cannot apply..." (Change shown in**bold**type.)

Activity CS•22, p. 106, question A2

- Part (a) should read: "Which state(s) has the
**highest**temperature? Explain." - Part (b) should read: "Which state(s) has the
**lowest**temperature? Explain." (Changes shown in**bold**type.)

Activity CS•26, p. 127, description for part B

- The springs being studied in this part of the activity are said to be "relaxed". This word should be omitted. Instead, the springs should be considered to have zero or very small relaxed length. The need for this change is that when the springs are relaxed initially, the balls attached to them in situation B1 would tend to move left and right as well as up and down, which is unnecessarily complicated. By making the relaxed length very small, the motion of the balls (in B1) becomes purely transverse, i.e., up and down. Note that this change affects only the results of B1.

Activity CS•30, p. 151, questions D3 and D4

- The question in D3 should read: "Will the wave form on the
**lighter**spring move faster or slower than the original wave form on the**heavier**spring?" - The question in D4 should begin: "Will the wave form on the
**lighter**spring..." (Changes shown in**bold**type.)

Reader/Chapter 1: Fluids, p. R18, table showing speeds of water outside holes

- The list of speeds in the last column are wrong. The correct table is shown below. (Right-click or command-click and choose "Open image in new window" or equivalent to see a full-sized version, then print at 50% to replace in student books.)

Reader/Chapter 1: Fluids, p. R19, table showing speeds of water outside holes and where the water lands

- The list of speeds in the third column and the list of where the water lands in the last column are wrong. The correct table is shown below. (Right-click or command-click and choose "Open image in new window" or equivalent to see a full-sized version, then print at 50% to replace in student books.)

*Many thanks to Prof. Josip Slisko of the Faculty of Physical and Mathematical Sciences at the Benemerita Public University in Puebla, Mexico, who found many of these mistakes.*