i Preface I: For Faculty v
ii Preface II: Students! Read Me! vii
ii.1 Studying vii
ii.2 Organization of the Book ix
1 Measurements 3
1.1 Coordinate systems 3
1.2 Dimensions and Units 3
1.3 Dimensional analysis 5
1.4 Error 6
1.5 Significant Figures 7
1.6 Discussion 9
1.7 Worked Problems 9
1.8 Homework Problems 10
1.9 Solutions to Worked Problems 11
2 Vectors 13
2.1 Introduction 13
2.2 Vector Multiplication 17
2.3 The Curie Principle 20
2.4 Discussion 20
2.5 Worked Problem 21
2.6 Homework 21
2.7 Solution to the Worked Problem 21
3 Calculus; Motion at Constant Acceleration 23
3.1 Introduction 23
3.2 The Standard Functions 23
3.3 Motion at Constant Acceleration 25
3.4 Discussion 30
3.5 Worked Problems 31
3.6 Homework 31
3.7 Solutions to the Worked Problems 35
4 Chapter 4. Averages, Average Velocity 37
4.1 Averages 37
4.2 Discussion 39
4.3 Worked Problems 39
4.4 Homework 40
4.5 Solutions to the Worked Problems 42
5 Derivatives of Vectors, Circular Motion 45
5.1 Introduction 45
5.2 Derivatives of Vectors: Cartesian Coordinates 45
5.3 Circular Motion 46
5.4 Ballistic Motion 48
5.5 Discussion 50
5.6 Worked Problems 50
5.7 Homework 50
5.8 Solutions to the Worked Problems 53
6 Newton’s Laws of Motion 55
6.1 Introduction 55
6.2 Newton’s Laws 55
6.3 Applications of Newton’s Laws 59
6.4 Discussion 63
6.5 Worked Problems 63
6.6 Homework 64
6.7 Solutions to the Worked Problems 69
7 Inertial and Non-Inertial Reference Frames 73
8 Applications of Newton’s Laws of Motion 77
8.1 Introduction 77
8.2 The Rocket Car on a Hill 77
8.3 Coupled Masses 80
8.4 The Hanging Mass 82
8.5 Worked Problems 84
8.6 Homework 85
8.7 Solutions to the Worked Problems 90
9 Tribology 95
9.1 Introduction 95
9.2 Kinetic Friction 96
9.3 Static Friction 98
9.4 Coupled Masses with Friction 99
9.5 Rolling Friction and the Tractive Force 102
9.6 Friction in Fluids 102
9.7 Discussion 104
9.8 Worked Problems 104
9.9 Homework 104
9.10 Solutions to the Worked Problems 108
10 Examination 1 113
10.1 Solutions to Examination I 115
11 Springs 119
11.1 Introduction 119
11.2 Forces On and By Springs 120
11.3 Hooke’s Law Springs 121
11.4 Spring Attached to Wall 124
11.5 Discussion 125
11.6 Worked Problems 126
11.7 Homework 126
11.8 Solutions to the Worked Problems 127
12 Momentum, Conservation, Collisions 131
12.1 The Center of Mass 131
12.2 Motion of a Group of Bodies 132
12.3 Collisions 133
12.4 Discussion 135
12.5 Worked Problems 135
12.6 Homework 136
12.7 Problem Solutions 137
13 Work, Kinetic Energy, and the Work-Energy Theorem 141
13.1 Work 141
13.2 The Work-Energy Theorem 142
13.3 Power 144
13.4 Examples of the Work-Energy Theorem 145
13.5 Worked Problems 149
13.6 Homework 150
13.7 Solutions to the Worked Problems 153
14 Energy 157
14.1 Introduction 157
14.2 Stability 159
14.3 Gravitational Potential Energy of an Extended Body 160
14.4 I Threw a Rock Into the Air 161
14.5 The Radical Roller Coaster 162
14.6 Two Masses Connected by a Wire 163
14.7 Potential Energy of a Spring 164
14.8 Discussion 165
14.9 Worked Problems 165
14.10 Homework 166
14.11 Solutions to the Worked Problems 170
15 Energy Conservation, Collisions, and Friction 175
15.1 Introduction 175
15.2 Examples of Collisions 176
15.3 Discussion 179
15.4 Worked Problems 180
15.5 Homework 180
15.6 Problem Solutions 182
16 Examination 2 183
16.1 Examination 2 Solutions 185
17 Descriptions of Rotation 187
17.1 Rotation 187
17.2 Vector Products 187
17.3 Circular Motion 189
17.4 Circular Motion in an Arbitrary Plane 191
17.5 Discussion 193
17.6 Worked Problems 193
17.7 Homework 193
17.8 Solutions to the Worked Problems 194
18 Motion in Cylindrical Polar Coordinates 197
18.1 Introduction 197
18.2 Worked Problems 201
18.3 Homework 201
18.4 Solutions to the Worked Problems 202
19 Angular Momentum 205
19.1 Introduction 205
19.2 Angular Momentum 205
19.3 Torque 206
19.4 Conservation of Angular Momentum 207
19.5 Displacement of the Origin 208
19.6 ω and L 209
19.7 Discussion 211
19.8 Worked Problems 211
19.9 Homework 212
19.10 Problem Solutions 214
20 Moment of Inertia 217
20.1 Introduction 217
20.2 Rigid Body Motion; Rolling Motion Without Slip 217
20.3 Composite Rotating Systems 219
20.4 Discussion 220
20.5 Worked Problems 220
20.6 Homework 220
20.7 Solutions to the Worked Problems 221
21 Rigid Body Rotation 223
21.1 Introduction 223
21.2 Example: The Physical Pendulum 223
21.3 Koenig’s Theorem 226
21.4 The Rolling Cylinder 226
21.5 Worked Problems 227
21.6 Homework 228
21.7 Solution to the Worked Problem 230
22 Torque Diagrams; Pendulums 233
22.1 The Torque Diagram 233
22.2 The Simple Pendulum 236
22.3 Pendulum with Extended Bob 237
22.4 Pendulum Motion: A Solution 239
22.5 Period of a Pendulum 240
22.6 Discussion 240
22.7 Worked Problems 241
22.8 Homework 241
22.9 Solutions to the Worked Problems 242
23 Coupled Motion Including Rotation 247
23.1 Introduction 247
23.2 One Mass and a Wheel 247
23.3 Two Masses and a Wheel 248
23.4 Discussion 252
23.5 Worked Problems 252
23.6 Homework 253
23.7 Problem Solutions 256
24 Statics 259
24.1 Simple Statics Problem 260
24.2 Ladder on a Wall with Friction 261
24.3 The Hinged Flagpole 262
24.4 Discussion 263
24.5 Worked Problems 264
24.6 Homework 265
24.7 Solutions to the Worked Problems 268
25 Gravity 273
25.1 Introduction 273
25.2 Newtonian Gravity 275
25.3 Escape Velocity 278
25.4 Weightlessness 279
25.5 Discussion 279
25.6 Worked Problems 280
25.7 Homework 280
25.8 Solutions to the Worked Problems 283
26 Planetary Orbits 287
26.1 Discussion 290
26.2 Worked Problem 290
26.3 Homework 290
26.4 Solution to the Worked Problem 291
27 Examination 3 293
27.1 Examination 3 Solutions 295
28 A Sequence of Experiments 301
29 Experiment One: Measurements are Imprecise 305
29.1 Experimental 305
29.2 Data Analysis 306
29.3 Making Graphs 308
29.4 The Search for Systematic Error 310
29.5 Laboratory Report 310
30 Experiment Two: The Search for Best Technique 313
30.1 Experimental 313
30.2 Data Analysis 314
30.3 Significant Figures 315
31 Experiment Three: Properties of the Pendulum 317
31.1 Data Fitting 317
32 Experiment Four: The Physical Pendulum 321
33 Experiment Five: The Atwood Machine 323
34 Experiment Six: The Static Force Diagram 325
35 Harmonic Motion 329
35.1 Note 330
36 Complex Numbers 331
36.1 Arithmetic with Complex Numbers 332
36.2 The Euler Identity 333
36.3 Note 334
36.4 Homework 334
37 Harmonic Oscillation 337
37.1 A Mass on a Spring 337
37.2 Canonical Forms for a Harmonic Oscillator 339
37.3 The Pendulum 340
37.4 Complex Variable Method 341
37.5 Energy of a Pendulum 342
37.6 Pendulums: Torque Approach 343
37.7 Physical Pendulum: Energy Approach 345
37.8 Calculating Constants of Integration 346
37.9 Homework 347
38 Harmonic Motion, Damped or Driven 351
38.1 Harmonic Oscillation with Damping 351
38.2 Energy Storage–The Quality Parameter 354
38.3 Harmonic Oscillation with an External Driving Force 355
38.4 Discussion 356
38.5 Homework 357
39 The Damped, Driven Harmonic Oscillator 359
39.1 Basic Calculation 359
39.2 Form of the Amplitude Curve 362
39.3 Power Absorption 365
39.4 Homework 369
40 Coupled Harmonic Oscillators 373
40.1 Mathematical Interlude 373
40.2 An Example 377
40.3 Discussion 379
40.4 Homework 379
41 The Double Pendulum 381
41.1 Discussion 384
41.2 Homework 384
42 The Oscillating String – Standing Waves 387
42.1 Normal Modes of a String 387
42.2 Energy in a Vibrating String 392
42.3 Homework 395
43 The Oscillating String – Traveling Waves 397
43.1 Introduction 397
43.2 Travelling Waves 397
43.3 Terminology 399
43.4 Longitudinal and Transverse Velocities 400
43.5 Homework 402
44 About the Author 405