Fundamentals of Physics: Mechanics, Relativity, and Thermodynamics

Content: 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.