Preface ...................................................... xiii
1 Strategies for solving problems .............................. 1
1.1 General strategies ...................................... 1
1.2 Units, dimensional analysis ............................. 4
1.3 Approximations, limiting cases .......................... 7
1.4 Solving differential equations numerically ............. 11
1.5 Problems ............................................... 14
1.6 Exercises .............................................. 15
1.7 Solutions .............................................. 18
2 Statics ..................................................... 22
2.1 Balancing forces ....................................... 22
2.2 Balancing torques ...................................... 27
2.3 Problems ............................................... 30
2.4 Exercises .............................................. 35
2.5 Solutions .............................................. 39
3 Using F = ma ................................................ 51
3.1 Newton's laws .......................................... 51
3.2 Free-body diagrams ..................................... 55
3.3 Solving differential equations ......................... 60
3.4 Projectile motion ...................................... 65
3.5 Motion in a plane, polar coordinates ................... 68
3.6 Problems ............................................... 70
3.7 Exercises .............................................. 75
3.8 Solutions .............................................. 84
4 Oscillations ............................................... 101
4.1 Linear differential equations ......................... 101
4.2 Simple harmonic motion ................................ 105
4.3 Damped harmonic motion ................................ 107
4.4 Driven (and damped) harmonic motion ................... 109
4.5 Coupled oscillators ................................... 115
4.6 Problems .............................................. 120
4.7 Exercises ............................................. 122
4.8 Solutions ............................................. 127
5 Conservation of energy and momentum ........................ 138
5.1 Conservation of energy in one dimension ............... 138
5.2 Small oscillations .................................... 147
5.3 Conservation of energy in three dimensions ............ 148
5.4 Gravity ............................................... 152
5.5 Momentum .............................................. 156
5.6 The center of mass frame .............................. 161
5.7 Collisions ............................................ 164
5.8 Inherently inelastic processes ........................ 167
5.9 Problems .............................................. 173
5.10 Exercises ............................................. 180
5.11 Solutions ............................................. 194
6 The Lagrangian method ...................................... 218
6.1 The Euler-Lagrange equations .......................... 218
6.2 The principle of stationary action .................... 221
6.3 Forces of constraint .................................. 227
6.4 Change of coordinates ................................. 229
6.5 Conservation laws ..................................... 232
6.6 Noether's theorem ..................................... 236
6.7 Small oscillations .................................... 239
6.8 Other applications .................................... 242
6.9 Problems .............................................. 246
6.10 Exercises ............................................. 251
6.11 Solutions ............................................. 255
7 Central forces ............................................. 281
7.1 Conservation of angular momentum ...................... 281
7.2 The effective potential ............................... 283
7.3 Solving the equations of motion ....................... 285
7.4 Gravity, Kepler's laws ................................ 287
7.5 Problems .............................................. 296
7.6 Exercises ............................................. 298
7.7 Solutions ............................................. 300
8 Angular momentum, Part I (Constant  ) ...................... 309
8.1 Pancake object in x-y plane ........................... 310
8.2 Nonplanar objects ..................................... 316
8.3 Calculating moments of inertia ........................ 318
8.4 Torque ................................................ 322
8.5 Collisions ............................................ 328
8.6 Angular impulse ....................................... 331
8.7 Problems .............................................. 333
8.8 Exercises ............................................. 339
8.9 Solutions ............................................. 349
9 Angular momentum, Part II (General ) ...................... 371
9.1 Preliminaries concerning rotations .................... 371
9.2 The inertia tensor .................................... 376
9.3 Principal axes ........................................ 383
9.4 Two basic types of problems ........................... 388
9.5 Euler's equations ..................................... 393
9.6 Free symmetric top .................................... 396
9.7 Heavy symmetric top ................................... 399
9.8 Problems .............................................. 415
9.9 Exercises ............................................. 421
9.10 Solutions ............................................. 428
10 Accelerating frames of reference ........................... 457
10.1 Relating the coordinates .............................. 458
10.2 The fictitious forces ................................. 460
10.3 Tides ................................................. 471
10.4 Problems .............................................. 477
10.5 Exercises ............................................. 482
10.6 Solutions ............................................. 486
11 Relativity (Kinematics) .................................... 501
11.1 Motivation ............................................ 502
11.2 The postulates ........................................ 509
11.3 The fundamental effects ............................... 511
11.4 The Lorentz transformations ........................... 523
11.5 Velocity addition ..................................... 529
11.6 The invariant interval ................................ 533
11.7 Minkowski diagrams .................................... 536
11.8 The Doppler effect .................................... 539
11.9 Rapidity .............................................. 543
11.10 Relativity without с ................................. 546
11.11 Problems ............................................. 549
11.12 Exercises ............................................ 556
11.13 Solutions ............................................ 565
12 Relativity (Dynamics) ...................................... 584
12.1 Energy and momentum ................................... 584
12.2 Transformations of E and p ............................ 594
12.3 Collisions and decays ................................. 596
12.4 Particle-physics units ................................ 600
12.5 Force ................................................. 601
12.6 Rocket motion ......................................... 606
12.7 Relativistic strings .................................. 609
12.8 Problems .............................................. 611
12.9 Exercises ............................................. 615
12.10 Solutions ............................................ 619
13 4-vectors .................................................. 634
13.1 Definition of 4-vectors ............................... 634
13.2 Examples of 4-vectors ................................. 635
13.3 Properties of 4-vectors ............................... 637
13.4 Energy, momentum ...................................... 639
13.5 Force and acceleration ................................ 640
13.6 The form of physical laws ............................. 643
13.7 Problems .............................................. 645
13.8 Exercises ............................................. 645
13.9 Solutions ............................................. 646
14 General Relativity ......................................... 649
14.1 The Equivalence Principle ............................. 649
14.2 Time dilation ......................................... 650
14.3 Uniformly accelerating frame .......................... 653
14.4 Maximal-proper-time principle ......................... 656
14.5 Twin paradox revisited ................................ 658
14.6 Problems .............................................. 660
14.7 Exercises ............................................. 663
14.8 Solutions ............................................. 666
Appendix A Useful formulas ................................... 675
Appendix В Multivariable, vector calculus .................... 679
Appendix C F = ma vs. F= dp/dt ............................... 690
Appendix D Existence of principal axes ....................... 693
Appendix E Diagonalizing matrices ............................ 696
Appendix F Qualitative relativity questions .................. 698
Appendix G Derivations of the Lν/c2 result ................... 704
Appendix H Resolutions to the twin paradox ................... 706
Appendix I Lorentz transformations ........................... 708
Appendix J Physical constants and data ....................... 711
References .................................................... 713
Index ......................................................... 716
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