preface xiii
chapter 1 introduction to the mechanical universe (program 1)
1.1 the copernican revolution
1.2 units and dimensions 5
1.3 a final word 10
chapter 2 the law of falling bodies (program 2) 13
2.1 aristotle's description of motion 13
2.2 do heavy bodies fall faster than lighter ones? 15
2.3 medieval laws of falling bodies 15
2.4 "the" law of falling bodies 20
2.5 the ave'rage speed of a falling body 25
2.6 instantaneous speed 26
2.7 acceleration 32
2.8 a final word 36
chapter 3 derivatives (program 3) 39
3.1 the development of differential calculus 39
3.2 the tangent line-derivative connection 41
3.3 rules of differentiation 47
3.4 derivatives of special functions 58
3.5 a final word 67
.chapter 4 inertia (program 4) 69
4.1 if the earth moves: aristotelian objections 6g
4.2 the earth moves: galileo's law of inertia 72
4.3 relative motion 75
4.4 projectile motion: a consequence of inertia 77
4.5 a final word 80
chapter 5 vectors (program 5) 81
5.1 the rise of vector analysis 81
5.2 vectors - a geometric view 82
5.3 vectors: an analytic view 96
5.4 the cross product 106
5.5 a final word 110
chapter 6 newton's laws (program 6) 111
6.1 the end of the confusion 111
6.2 newton's laws of motion 112
6.3 units of mass, momentum, and force 117
6.4 projectile motion:an application of-newton's second law 119
6.5 a final word 127
chapter 7 integration (program 7) 129
7.1 antidifferentiation, the reverse of differentiation 129
7.2 antidifferentiation and quadrature 133
7.3 the leibniz integral notation 137
7.4 applications of the second fundamental theorem to physics 145
7.5 a final word 150
appendix 1 the fundamental theorems of calculus 151
appendix 2 quadrature of a hyperbolic segment. the logarithm function 152
chapter 8 the apple and the moon (program 8) 159
8.1 the genesis of an idea 159
8.2 the law of universal gravitation 160
8.3 acceleration of gravity on the earth ? 65
8.4 why the moon doesn't fall to the earth 168
8.5 a final word 172
chapter 9 moving in circles (program 9) 175
9.1 the perfection of circular motion 175
9.2 derivatives of vector functions 177
9.3 uniform circular motion 183
9.4 circular orbits 187
9.5 motion along space curves 189
9.6 a final word 191
chapter 10 forces (program 10) 193
10.1 the fundamental forces 193
10.2 gravitational and electric forces 195
10.3 contact forces 198
10.4 application of newton's laws 202
10.5 friction 210
10.6 a final word 215
chapter 11 gravity, electricity, and magnetism (program 11) 217
11.1 finding the connection between electricity and magnetism 217
11.2 faraday's fields 219
11.3 a prediction from electromagnetism 224
11.4 a final word 226
chapter 12 the millikan oil-drop experiment (program 12) 229
12.1 the discovery of the electron 229
12.2 motion in a resistive medium 233
12.3 theoii-drop experiment 239
12.4 a final word 243
chapter 13 the law of conservation of energy (program 13) 245
13.1 toward an idea of energy 245
13.2 work and potential energy 247
13.3 the law of conservation of energy 252
13.4 heat and energy 260
13.5 a final word 263
chapter 14 energy and stability (program 14) 267
14.1 forms of energy 267
14.2 gravitational potential energy 274
14.3 potential energy and stability 278
14.4 a final word 284
chapter 15 temperature and the gas laws (program 45) 287
15.1 temperature and pressure 287
15.2 the gas laws of boyle, charles, and gay-lussac 293
15.3 the ideal-gas law 295
15.4 temperature and energy 297
15.5 a final word 299
chapter 16 the engine of nature (program 46) 301
16.1 the age of steam 301
16.2 work and the pressure-volume diagram 303
16.3 the first law of thermodynamics 309
16.4 adiabatic and isothermal processes 312
16.5 the second law of thermodynamics 316
16.6 the carnot engine 319
16.7 a final word 324
chapter 17 entropy (program 47) 327
17.1 toward an understanding of entropy 327
17.2 engines and entropy 330
17.3 entropy and the second law of thermodynamics 336
17.4 an implication of the entropy principle 338
17.5 a final word 341
chapter 18 the quest for low temperatures (program 48) 343
18.1 cooling off 343
18.2 thestates of matter 344
18.3 behavior of water 349
18.4 liquefaction of gases 351
18.5 the joule-thomson effect 355
18.6 a final word 357
chapter 19 the conservation of momentum{program 15) 359
19.1 the universe as a machine 359
19.2 newton's laws in retrospect 360
19.3 the law of conservation of momentum 364
19.4 applications of conservation of momentum 368
19.5 collision forces and times 376
19.6 a final word 378
chapter 20 harmonic motion (program 16) 379
20.1 finding a clock that wouldn't get seasick 379
20.2 simple harmonic motion 381
20.3 energy conservation and simple harmonic motion 387
20.4 initial conditions 390
20.5 the simple pendulum 393
20.6 a final word 396
chapter 21 resonance (program 17) 399
21.1 forced oscillations 399
21.2 describing resonance 401
21.3 swinging and singing wires in the wind 408
21.4 a final word 409
chapter 22 coupled oscillators and waves (program 18) 413
22.1 newton and the speed of sound 413
22.2 coupled oscillators 415
22.3 water waves and wave characteristics 417
22.4 wave speed 420
22.5 sound 426
22.6 sound intensities 428
22.7 sound and heat 429
22.8 a final word 430
chapter 23 angular momentum (program 19) 433
23.1 the search for order 433
23.2 the law of equal areas 437
23.3 angular momentum 440
23.4 torque and angular momentum 444
23.5 vortices and firestorms 447
23.6 angular momentum and the architecture of the heavens 450
23.7 a final word 454
chapter 24 gyroscopes (program 20) 457
24.1 an ancient question 457
24.2 the gyroscope 459
24.3 the gyrocompass 466
24.4 angular velocity of precession 469
24.5 the earth as a gyrosc.ope 473
24.6 a final word 474
chapter 25 kepler's laws and the conic sections (program 21) 477
25.1 the quest for precision 477
25.2 kepler's laws 479
25.3 conic sections 482
25.4 the ellipse 485
25.5 the conics and eccentricity 489
25.6 cartesian equations for conic sections 492
25.7 a final word 494
chapter 26 solving the kepler problem (program 22) 497
26.1 setting the*stage 497
26.2 polar coordinates and the unit vectors r and o 499
26.3 solution of the kepler problem 502
26.4 a final word 504
chapter 27 energy and eccentricity (program 23) 507
27. l celestial omens: comets 507
27.2 energy in space 508
27.3 energy and eccentricity 511
27.4 orbits and eccentricity 513
27.5 planetary motion and effective potential 516
27.6 calculating the orbit from initial conditions 519
27.7 a final word 522
chapter 28 navigating in space (program 24) 525
28.1 freeways in the sky 525
28.2 navigating in space 526
28.3 transfer orbits 529
28.4 gravity assist 534
28.5 a final word 537
chapter 29 loose ends and black holes (program 25) 539
29.1 kepler's third law 539
29.2 the earth-sun and earth-moon systems 541
29.3 the tides 543
29.4 the principle of equivalence 546
29.5 einstein's theory of gravity 548
29.6 black holes 549
29.7 a final word 550
chapter 30 the harmony of the spheres: an overview of the
mechanical universe (program 26) 553
30.1 winding up the mechanical universe 553
30.2 the physics of the heavens and earth 554
30.3 the language of physics 556
30.4 the conservation laws of the mechanical universe 559
30.5 a final word 561
appendix a the international system of units 563
appendix b conversion factors 565
appendix c formulas from algebra, geometry, and trigonometry 569
appendix d astronomical data 571
appendix e physical constants 573
selected bibliography 575
index 579
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