Fundamentals of Physics I Mechanics Relativity and Thermodynamics 1st Edition by R Shankar ISBN 9780300249583 0300249586

1. The Structure of Mechanics

1.1. Introduction and some useful tips

1.2. Kinematics and dynamics

1.3. Average and instantaneous quantities

1.4. Motion at constant acceleration

1.5. Sample problem

1.6. Deriving v2 − v20 = 2a(x – x0) using calculus

2. Motion in Higher Dimensions

2.1. Review

2.2. Vectors in d = 2

2.3. Unit vectors

2.4. Choice of axes and basis vectors

2.5. Derivatives of the position vector r

2.6. Application to circular motion

2.7. Projectile motion

3. Newton’s Laws I

3.1. Introduction to Newton’s laws of motion

3.2. Newton’s second law

3.3. Two halves of the second law

3.4. Newton’s third law

3.5. Weight and weightlessness

4. Newton’s Laws II

4.1. A solved example

4.2. Never the whole story

4.3. Motion in d = 2

4.4. Friction: static and kinetic

4.5. Inclined plane

4.6. Coupled masses

4.7. Circular motion, loop-the-loop

5. Law of Conservation of Energy

5.1. Introduction to energy

5.2. The work-energy theorem and power

5.3. Conservation of energy: K2 + U2 = K1 + U1

5.4. Friction and the work-energy theorem

6. Conservation of Energy in d = 2

6.1. Calculus review

6.2. Work done in d = 2

6.3. Work done in d = 2 and the dot product

6.4. Conservative and non-conservative forces

6.5. Conservative forces

6.6. Application to gravitational potential energy

7. The Kepler Problem

7.1. Kepler’s laws

7.2. The law of universal gravity

7.3. Details of the orbits

7.4. Law of conservation of energy far from the earth

7.5. Choosing the constant in U

8. Multi-particle Dynamics

8.1. The two-body problem

8.2. The center of mass

8.3. Law of conservation of momentum

8.4. Rocket science

8.5. Elastic and inelastic collisions

8.6. Scattering in higher dimensions

9. Rotational Dynamics I

9.1. Introduction to rigid bodies

9.2. Angle of rotation, the radian

9.3. Rotation at constant angular acceleration

9.4. Rotational inertia, momentum, and energy

9.5. Torque and the work-energy theorem

9.6. Calculating the moment of inertia

10. Rotational Dynamics II

10.1. The parallel axis theorem

10.2. Kinetic energy for a general N-body system

10.3. Simultaneous translations and rotations

10.4. Conservation of energy

10.5. Rotational dynamics using τ = dL/dt

10.6. Advanced rotations

10.7. Conservation of angular momentum

10.8. Angular momentum of the figure skater

11. Rotational Dynamics III

11.1. Static equilibrium

11.2. The seesaw

11.3. A hanging sign

11.4. The leaning ladder

11.5. Rigid-body dynamics in 3d

11.6. The gyroscope

12. Special Relativity I: The Lorentz Transformation

12.1. Galilean and Newtonian relativity

12.2. Proof of Galilean relativity

12.3. Enter Einstein

12.4. The postulates

12.5. The Lorentz transformation

13. Special Relativity II: Some Consequences

13.1. Summary of the Lorentz transformation

13.2. The velocity transformation law

13.3. Relativity of simultaneity

13.4. Time dilatation

13.4.1. Twin paradox

13.4.2. Length contraction

13.5. More paradoxes

13.5.1. Too big to fall

13.5.2. Muons in flight

14. Special Relativity III: Past, Present, and Future

14.1. Past, present, and future in relativity

14.2. Geometry of spacetime

14.3. Rapidity

14.4. Four-vectors

14.5. Proper time

15. Four-momentum

15.1. Relativistic scattering

15.1.1. Compton effect

15.1.2. Pair production

15.1.3. Photon absorption

16. Mathematical Methods

16.1. Taylor series of a function

16.2. Examples and issues with the Taylor series

16.3. Taylor series of some popular functions

16.4. Trigonometric and exponential functions

16.5. Properties of complex numbers

16.6. Polar form of complex numbers

17. Simple Harmonic Motion

17.1. More examples of oscillations

17.2. Superposition of solutions

17.3. Conditions on solutions to the harmonic oscillator

17.4. Exponential functions as generic solutions

17.5. Damped oscillations: a classification

17.5.1. Over-damped oscillations

17.5.2. Under-damped oscillations

17.5.3. Critically damped oscillations

17.6. Driven oscillator

18. Waves I

18.1. The wave equation

18.2. Solutions of the wave equation

18.3. Frequency and period

19. Waves II

19.1. Wave energy and power transmitted

19.2. Doppler effect

19.3. Superposition of waves

19.4. Interference: the double-slit experiment

19.5. Standing waves and musical instruments

20. Fluids

20.1. Introduction to fluid dynamics and statics

20.1.1. Density and pressure

20.1.2. Pressure as a function of depth

20.2. The hydraulic press

20.3. Archimedes’ principle

20.4. Bernoulli’s equation

20.4.1. Continuity equation

20.5. Applications of Bernoulli’s equation

21. Heat

21.1. Equilibrium and the zeroth law: temperature

21.2. Calibrating temperature

21.3. Absolute zero and the Kelvin scale

21.4. Heat and specific heat

21.5. Phase change

21.6. Radiation, convection, and conduction

21.7. Heat as molecular kinetic energy

22. Thermodynamics I

22.1. Recap

22.2. Boltzmann’s constant and Avogadro’s number

22.3. Microscopic definition of absolute temperature

22.4. Statistical properties of matter and radiation

22.5. Thermodynamic processes

22.6. Quasi-static processes

22.7. The first law of thermodynamics

22.8. Specific heats: cv and cp

23. Thermodynamics II

23.1. Cycles and state variables

23.2. Adiabatic processes

23.3. The second law of thermodynamics

23.4. The Carnot engine

23.4.1. Defining T using Carnot engines

24. Entropy and Irreversibility

24.1. Entropy

24.2. The second law: law of increasing entropy

24.3. Statistical mechanics and entropy

24.4. Entropy of an ideal gas: full microscopic analysis

24.5. Maximum entropy principle illustrated

24.6. The Gibbs formalism

24.7. The third law of thermodynamics

Exercises

Problem Set 1, for Chapter 1

Problem Set 2, for Chapter 2

Problem Set 3, for Chapters 3 and 4

Problem Set 4, for Chapters 5, 6, and 7

Problem Set 5, for Chapter 8

Problem Set 6, for Chapters 9, 10, and 11

Problem Set 7, for Chapters 12, 13, 14, and 15

Problem Set 8, for Chapters 16 and 17

Problem Set 9, for Chapters 18 and 19

Problem Set 10, for Chapter 20

Problem Set 11, for Chapters 21, 22, 23, and 24

Answers to Exercises

Problem Set 1, for Chapter 1

Problem Set 2, for Chapter 2

Problem Set 3, for Chapters 3 and 4

Problem Set 4, for Chapters 5, 6, and 7

Problem Set 5, for Chapter 8

Problem Set 6, for Chapters 9, 10, and 11

Problem Set 7, for Chapters 12, 13, 14, and 15

Problem Set 8, for Chapters 16 and 17

Problem Set 9, for Chapters 18 and 19

Problem Set 10, for Chapter 20

Problem Set 11, for Chapters 21, 22, 23, and 24

Constants and Other Data

Index