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)