**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,

*. 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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