Fundamentals of physics: mechanics, relativity, and thermodynamics

1. The structure of mechanics. Kinematics and dynamics

Average and instantaneous quantities

Motion at constant acceleration

2. Motion in higher dimensions. Vectors in d=2

Unit vectors

Choice of axes and basis vectors

Derivatives of the position vector r

Application to circular motion

Projectile motion

3. Newton's laws I. Introduction of Newton's laws of motion

Newton's second law

Two halves of the second law

Newton's third law

Weight and weightlessness

4. Newton's laws II. Motion in d=2

Friction : static and kinetic

Inclined plane

Coupled masses

Circular motion, loop-the-loop

5. Law of conservation of energy. The work-energy theorem and power

Friction and the work-energy theorem

6. Conservation of energy in d=2. Work done in d=2 and the dot product

Conservative and non-conservative forces

Application to gravitational potential energy

7. The Kepler problem. Kepler's laws

The law of universal gravity

Details of the orbits

Law of conservation of energy far from the earth

Choosing the constant in U

8. Multi-particle dynamics. The two-body problem

The center of mass

Law of conservation of momentum

Rocket science

Elastic and inelastic collisions

Scattering in higher dimensions

9. Rotational dynamics I. Introduction to rigid bodies

Angle of rotation, the radian

Rotation at constant angular acceleration

Rotational inertia, momentum, and energy

Torque and the work-energy theorem

Calculating the moment of inertia

10. Rotational dynamics II. The parallel axis theorem

Kinetic energy for a general N-body system

Simultaneous translations and rotations

Conservation of energy

Advanced rotations

Conservation of angular momentum

Angular momentum of the figure skater

11. Rotational dynamics III. Static equilibrium

The seesaw

A hanging sign

The leaning ladder

Rigid-body dynamics in 3d

The gyroscope

12. Special relativity I : the Lorentz transformation. Galilean and Newtonian relativity

Proof of Galilean relativity

Enter Einstein

The postulates

The Lorentz transformation

13. Special relativity II : some consequences. The velocity transformation law

Relativity of simultaneity

Time dilation

More paradox

14. Special relativity III : past, present, and future. Past, present, and future in relativity

Geometry of spacetime

Rapidity

Four-vectors

Proper time

15. Four-momentum. Relativistic scattering

16. Mathematical methods. Taylor series of a function

Trigonometric and exponential functions

Properties of complex numbers

Polar form of complex numbers

17. Simple harmonic motion. More examples of oscillations

Superposition of solutions

Conditions on solutions to the harmonic oscillator

Exponential functions as generic solutions

Damped oscillations : a classification

Driven oscillator

18. Waves I. The wave equation

Frequency and period

19. Waves II. Wave energy and power transmitted

Doppler effect

Superposition of waves

Interference : double-slit experiment

Standing waves and musical instruments

20. Fluids. Introduction to fluid dynamics and statics

The hydraulic press

Archimedes' principle

Bernoulli's equation

Applications of Bernoulli's equation

21. Heat. Equilibrium and the zeroth law : temperature

Calibrating temperature

Absolute zero and the Kelvin scale

Heat and specific heat

Phase change

Radiation, convection, and conduction

Heat as molecular kinetic energy

22. Thermodynamics I. Boltzmann's constant and Avogadro's number

Microscopic definition of absolute temperature

Statistical properties of matter and radiation

Thermodynamic processes

Quasi-static processes

The first law of thermodynamics

23. Thermodynamics II. Cycles and state variables

Adiabatic processes

The second law of thermodynamics

The Carnot engine

24. Entropy and irreversibility. Entropy

The second law : law of increasing entropy

Statistical mechanics and entropy

Entropy of an ideal gas : full microscopic analysis

Maximum entropy principle illustrated

The Gibbs formalism

The third law of thermodynamics.