1: Motion

How to Use This Book    xi

Acknowledgments    xiii

Activities

• 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

Reader: Chapter 1—Describing Motion    R1

• 1.0 Introduction    R1
  • six terms used to describe motion    R1
• 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
    • representing the position in two dimensions    R3
      • magnitude & direction    R3,4
      • component representation    R4
      • directed line segment    R4
    • why we use three different representations    R4
  • Using graphs to describe the position of objects moving in one dimension    R5
• 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
  • Displacement in two dimensions    R7
• 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
  • 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
  • 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
  • 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
  • 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
• 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
  • 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
  • Representing and interpreting acceleration in one dimension    R24,25
    • using directed line segments for velocity    R24
    • using a number line for velocity    R25
  • 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
  • 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
    • 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
• 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
  • 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
  • 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
  • Conclusion    R36
    • why problem solving is so difficult    R36
    • how to simplify kinematics problems    R36
    • why understanding motion is so important    R36

1-TG: Teacher's Guide to Motion

2: Interactions

How to Use this Book    xi

Acknowledgments    xiii

Activities

• 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

Reader: Chapter 2 — Describing Interactions

• 2.0 Introduction    R37
  • What is meant by dynamics?    R37
  • Why is acceleration such an important concept?    R37
• 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
  • 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
  • Measuring forces    R38
    • explaining why springs are preferred for measuring forces    R38
    • importance of knowing what a scale is actually measuring    R38
  • Units of force    R38
    • introducing the pound (lb) and the newton (N)    R38
    • converting from one unit of force to another    R38
  • Identifying forces    R39-41
    • identifying the objects interacting    R39
    • identifying the type of interaction    R39,40
    • determining the direction of a force    R40,41
  • 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
  • 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
  • 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
  • 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 net force    R46
    • definition of net force    R46
• 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
  • 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
    • 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
    • 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
  • 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
  • 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
• 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
  • 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
  • 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
  • Conclusion    R60

Appendix: Table of Common Forces

• 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
  • Air resistance force (also called Drag force)    A4
• Action-at-a-distance Forces    A5,6
  • Gravitational force    A5
    • near the surface of the Earth    A5
    • Universal Law of Gravitation    A5
  • Electrostatic force    A6
  • Magnetic force    A6

2-TG: Teacher's Guide to Interactions

3: Conservation Laws & Concept-Based Problem Solving

How to Use this Book    xiii

Acknowledgments    xv

Activities

• 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

Reader: Chapter 3 — Conservation Laws

• 3.0 Introduction    R61
  • What is meant by a conservation law?    R61
  • Why use a conservation law instead of dynamics?    R61
• 3.1 SYSTEMS    R61
  • What is a system?    R61
  • Sizes of systems    R61
• 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
  • 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
• 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
  • 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
• 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
    • 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
  • 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
    • 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
  • Summary of momentum ideas and principles    R79
    • one new state quantity: momentum p    R79
    • two new process quantities: impulse J, and change in momentum Dp    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
• 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
  • 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
    • 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
    • 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
    • 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
    • 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
  • 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
• 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
  • 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
  • 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
  • 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
• 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
  • 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
• 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
  • 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
  • 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
  • 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

Reader: Chapter 4 — Concept-Based Problem Solving

• 4.0 Introduction    R115
  • Some questions you might ask yourself before solving a problem    R115
  • Why a conceptual analysis should precede equation manipulation    R115
• 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
  • 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
  • Interconnecting ideas in mechanics    R121
    • using concepts to organize knowledge    R121
• 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
    • solution to the sample problem    R122,123
  • 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
  • Conclusion    R126
    • representation of the concept-based problem-solving approach    R126

3-TG: Teacher's Guide to Conservation Laws & Concept-Based Problem Solving

FF: Fundamental Forces & Fields

How to Use this Book    xv

Acknowledgments    xvii

Activities

• 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

Reader: Fundamental Forces and Fields

• 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
• 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
  • 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
  • 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
  • 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
  • 1.5. Applying the simplified model of electric interactions    R7
    • An example showing how the model can predict the behavior of something    R7
  • 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
  • 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
  • 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
  • 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
  • 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
  • 1.11 Applying our simplified model of magnetic interactions    R14
    • Examples of how to apply this model of magnetic interactions    R14
  • 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
  • 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
  • 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
  • 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
  • 1.16 Mass vs. weight    R19
    • differences between mass and weight    R19
  • 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
• 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 2.9. Reasoning with Universal gravitation    R32,33
    • examples showing how to reason using Universal gravitation    R32,33
  • 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
• 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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 Fm    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
  • 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
  • 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
  • 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
  • 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
• 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
  • 4.2. Solving problems using Newton's laws    R48,49
    • an example involving the magnetic interaction    R48,49
  • 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
  • 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

FF-TG: Teacher's Guide to Fundamental Forces & Fields

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

AT: Advanced Topics in Mechanics

How to Use this Book    xv

Acknowledgments    xvii

Activities

• 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

Reader: Advanced Topics in Mechanics

• 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
    • 1.1.2. Newton's laws and uniform circular motion    R4
      • relationship between net force and acceleration    R4
    • 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
    • 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
    • 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
    • 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
  • 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
    • 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
    • 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
    • 1.2.4. Free-fall acceleration    R14
      • difference between g and a_g    R14
      • why we use the symbol a_g to denote free-fall acceleration    R14
    • 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
    • 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
    • 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
      • 2 examples    R19,20
      • how to interpret a negative root    R20
    • 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
  • 1.3. RELATIVE MOTION    R23-35
    • situations covered by relative motion    R23
      • some goals of studying relative motion    R23
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
      • sometimes, a situation is easier to analyze in one frame than another    R32,33
    • 1.3.9. Solving problems with relative motion ideas    R33-35
      • many common problems involve navigation    R33,34
      • definition of the term heading    R35
• 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
    • 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
    • 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
    • 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
    • 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
  • 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
    • 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
    • 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
    • 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
    • 2.2.5. Angular vs. linear dynamics    R48
      • table comparing linear and angular dynamics    R48
    • 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
    • 2.2.7. Solving problems in angular dynamics    R51
      • an example    R51
      • relationship between angular acceleration and linear acceleration    R51
  • 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
    • 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
    • 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
    • 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
    • 2.3.5. 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
  • 2.4. SOLVING PROBLEMS IN ROTATIONAL MOTION    R56
    • general guidelines for solving problems in rotational motion    R56

AT-TG: Teacher's Guide to Advanced Topics in Mechanics

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CS: Complex Systems

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CS-TG: Teacher's Guide to Complex Systems

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