Fundamentals of Physics I: Mechanics, Relativity, and Thermodynamics by R. Shankar, ISBN-13: 978-0300243772
[PDF eBook eTextbook]
- Publisher: Yale University Press; Expanded edition (August 20, 2019)
- Language: English
- 528 pages
- ISBN-10: 0300243774
- ISBN-13: 978-0300243772
A beloved introductory physics textbook, now including exercises and an answer key, explains the concepts essential for thorough scientific understanding.
In this concise book, R. Shankar, a well‑known physicist and contagiously enthusiastic educator, explains the essential concepts of Newtonian mechanics, special relativity, waves, fluids, thermodynamics, and statistical mechanics. Now in an expanded edition—complete with problem sets and answers for course use or self‑study—this work provides an ideal introduction for college‑level students of physics, chemistry, and engineering; for AP Physics students; and for general readers interested in advances in the sciences. The book begins at the simplest level, develops the basics, and reinforces fundamentals, ensuring a solid foundation in the principles and methods of physics.
Table of Contents:
Preface to the Expanded Edition xiii
Preface to the First Edition xiv
1. The Structure of Mechanics 1
1.1 Introduction and some useful tips 1
1.2 Kinematics and dynamics 2
1.3 Average and instantaneous quantities 4
1.4 Motion at constant acceleration 6
1.5 Sample problem 10
1.6 Deriving v2 −v2
0
= 2a(x −x0) using calculus 13
2. Motion in Higher Dimensions 15
2.1 Review 15
2.2 Vectors in d =2 16
2.3 Unit vectors 19
2.4 Choice of axes and basis vectors 22
2.5 Derivatives of the position vector r 26
2.6 Application to circular motion 29
2.7 Projectile motion 32
3. Newton’s Laws I 36
3.1 Introduction to Newton’s laws of motion 36
3.2 Newton’s second law 38
3.3 Two halves of the second law 41
3.4 Newton’s third law 45
3.5 Weight and weightlessness 49
4. Newton’s Laws II 51
4.1 A solved example 51
4.2 Never the whole story 54
4.3 Motion in d =2 55
4.4 Friction: static and kinetic 56
4.5 Inclined plane 57
4.6 Coupled masses 61
4.7 Circular motion, loop-the-loop 64
5. Law of Conservation of Energy 70
5.1 Introduction to energy 70
5.2 The work-energy theorem and power 71
5.3 Conservation of energy: K2 +U2 = K1 +U1 75
5.4 Friction and the work-energy theorem 78
6. Conservation of Energy in d =2 82
6.1 Calculus review 82
6.2 Work done in d =2 84
6.3 Work done in d = 2 and the dot product 88
6.4 Conservative and non-conservative forces 92
6.5 Conservative forces 95
6.6 Application to gravitational potential energy 98
7. The Kepler Problem 101
7.1 Kepler’s laws 101
7.2 The law of universal gravity 104
7.3 Details of the orbits 108
7.4 Law of conservation of energy far from the earth 112
7.5 Choosing the constant in U 114
8. Multi-particle Dynamics 118
8.1 The two-body problem 118
8.2 The center of mass 119
8.3 Law of conservation of momentum 128
8.4 Rocket science 134
8.5 Elastic and inelastic collisions 136
8.6 Scattering in higher dimensions 140
9. Rotational Dynamics I 143
9.1 Introduction to rigid bodies 143
9.2 Angle of rotation, the radian 145
9.3 Rotation at constant angular acceleration 147
9.4 Rotational inertia, momentum, and energy 148
9.5 Torque and the work-energy theorem 154
9.6 Calculating the moment of inertia 156
10. Rotational Dynamics II 159
10.1 The parallel axis theorem 159
10.2 Kinetic energy for a general N-body system 163
10.3 Simultaneous translations and rotations 165
10.4 Conservation of energy 167
10.5 Rotational dynamics using τ = dL
dt 168
10.6 Advanced rotations 169
10.7 Conservation of angular momentum 171
10.8 Angular momentum of the figure skater 172
11. Rotational Dynamics III 175
11.1 Static equilibrium 175
11.2 The seesaw 176
11.3 A hanging sign 178
11.4 The leaning ladder 180
11.5 Rigid-body dynamics in 3d 182
11.6 The gyroscope 191
12. Special Relativity I: The Lorentz Transformation 194
12.1 Galilean and Newtonian relativity 195
12.2 Proof of Galilean relativity 196
12.3 Enter Einstein 200
12.4 The postulates 203
12.5 The Lorentz transformation 204
13. Special Relativity II: Some Consequences 209
13.1 Summary of the Lorentz transformation 209
13.2 The velocity transformation law 212
13.3 Relativity of simultaneity 214
13.4 Time dilatation 216
13.4.1 Twin paradox 219
13.4.2 Length contraction 220
13.5 More paradoxes 222
13.5.1 Too big to fall 222
13.5.2 Muons in flight 226
14. Special Relativity III: Past, Present, and Future 227
14.1 Past, present, and future in relativity 227
14.2 Geometry of spacetime 232
14.3 Rapidity 235
14.4 Four-vectors 238
14.5 Proper time 239
15. Four-momentum 241
15.1 Relativistic scattering 249
15.1.1 Compton effect 249
15.1.2 Pair production 251
15.1.3 Photon absorption 252
16. Mathematical Methods 255
16.1 Taylor series of a function 255
16.2 Examples and issues with the Taylor series 261
16.3 Taylor series of some popular functions 263
16.4 Trigonometric and exponential functions 265
16.5 Properties of complex numbers 267
16.6 Polar form of complex numbers 272
17. Simple Harmonic Motion 275
17.1 More examples of oscillations 280
17.2 Superposition of solutions 283
17.3 Conditions on solutions to the harmonic oscillator 288
17.4 Exponential functions as generic solutions 290
17.5 Damped oscillations: a classification 291
17.5.1 Over-damped oscillations 291
17.5.2 Under-damped oscillations 292
17.5.3 Critically damped oscillations 294
17.6 Driven oscillator 294
18. Waves I 303
18.1 The wave equation 306
18.2 Solutions of the wave equation 310
18.3 Frequency and period 313
19. Waves II 316
19.1 Wave energy and power transmitted 316
19.2 Doppler effect 320
19.3 Superposition of waves 323
19.4 Interference: the double-slit experiment 326
19.5 Standing waves and musical instruments 330
20. Fluids 335
20.1 Introduction to fluid dynamics and statics 335
20.1.1 Density and pressure 335
20.1.2 Pressure as a function of depth 336
20.2 The hydraulic press 341
20.3 Archimedes’ principle 343
20.4 Bernoulli’s equation 346
20.4.1 Continuity equation 346
20.5 Applications of Bernoulli’s equation 349
21. Heat 352
21.1 Equilibrium and the zeroth law: temperature 352
21.2 Calibrating temperature 354
21.3 Absolute zero and the Kelvin scale 360
21.4 Heat and specific heat 361
21.5 Phase change 365
21.6 Radiation, convection, and conduction 368
21.7 Heat as molecular kinetic energy 371
22. Thermodynamics I 375
22.1 Recap 375
22.2 Boltzmann’s constant and Avogadro’s number 376
22.3 Microscopic definition of absolute temperature 379
22.4 Statistical properties of matter and radiation 382
22.5 Thermodynamic processes 384
22.6 Quasi-static processes 386
22.7 The first law of thermodynamics 387
22.8 Specific heats: cv and cp 391
23. Thermodynamics II 394
23.1 Cycles and state variables 394
23.2 Adiabatic processes 396
23.3 The second law of thermodynamics 399
23.4 The Carnot engine 403
23.4.1 Defining T using Carnot engines 409
24. Entropy and Irreversibility 411
24.1 Entropy 411
24.2 The second law: law of increasing entropy 418
24.3 Statistical mechanics and entropy 423
24.4 Entropy of an ideal gas: full microscopic analysis 430
24.5 Maximum entropy principle illustrated 434
24.6 The Gibbs formalism 437
24.7 The third law of thermodynamics 441
Exercises 443
Problem Set 1, for Chapter 1 443
Problem Set 2, for Chapter 2 446
Problem Set 3, for Chapters 3 and 4 449
Problem Set 4, for Chapters 5, 6, and 7 455
Problem Set 5, for Chapter 8 458
Problem Set 6, for Chapters 9, 10, and 11 461
Problem Set 7, for Chapters 12, 13, 14, and 15 466
Problem Set 8, for Chapters 16 and 17 470
Problem Set 9, for Chapters 18 and 19 475
Problem Set 10, for Chapter 20 478
Problem Set 11, for Chapters 21, 22, 23, and 24 481
Answers to Exercises 487
Problem Set 1, for Chapter 1 487
Problem Set 2, for Chapter 2 488
Problem Set 3, for Chapters 3 and 4 489
Problem Set 4, for Chapters 5, 6, and 7 491
Problem Set 5, for Chapter 8 491
Problem Set 6, for Chapters 9, 10, and 11 492
Problem Set 7, for Chapters 12, 13, 14, and 15 494
Problem Set 8, for Chapters 16 and 17 495
Problem Set 9, for Chapters 18 and 19 497
Problem Set 10, for Chapter 20 498
Problem Set 11, for Chapters 21, 22, 23, and 24 498
Constants and Other Data 501
Index 503
R. Shankar is Josiah Willard Gibbs Professor of Physics, Yale University. He is winner of the American Physical Society’s Lilienfeld Prize and author of five textbooks, including Principles of Quantum Mechanics, Basic Training in Mathematics, and Quantum Field Theory and Condensed Matter Physics.
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