Physics

Waves and thermodynamics

Oscillation, waves, sound, heat, entropy.

Basics

Simple harmonic motion

If restoring force is proportional and opposite to displacement (F=−kx), motion is SHM. Ideal period does not depend on amplitude. A wave transports energy through a medium (or fields).

Laws of thermodynamics

Zeroth: thermal equilibrium is transitive (defines temperature). First: ΔU = Q − W (watch the sign convention). Second: entropy of an isolated system does not decrease. Heat does not flow unaided from cold to hot.

Formulas

Spring period

T = 2π √(m / k)

Heavier mass or softer spring → longer period.

Symbols

T period

Simple pendulum (small angle)

T = 2π √(L / g)

Depends on length and g, not mass or small amplitude.

Symbols

L length

Wave relation

v = f λ, f = 1 / T

Speed = frequency × wavelength. The medium often sets the speed.

Symbols

f frequency (Hz)
λ wavelength

Snell's law

n₁ sin θ₁ = n₂ sin θ₂

Refraction at a boundary. n = c / v.

Symbols

n refractive index

Monatomic ideal-gas internal energy

U = (3/2) n R T

For an ideal gas, U depends only on temperature (kinetic energy).

Carnot efficiency

η = 1 − T_C / T_H

Upper bound for a heat engine between two reservoirs. Temperatures in kelvin.

Symbols

T_H hot reservoir T
T_C cold reservoir T

In this field

Mechanics

Kinematics, Newton, momentum, circular motion.

Energy and work

Work, kinetic and potential energy, power, conservation.

Electromagnetism and modern physics

Charge, fields, basic circuits, photons, mass–energy.

Fluids and optics

Pressure, buoyancy, Bernoulli, lenses, interference.

Relativity and nuclear sketch

Time dilation, length contraction, decay, cross-section.

Quantum sketch

Photons, matter waves, uncertainty.

Gravity and orbits

Newton's gravity, Kepler, surface g, and circular orbits.

Rotation

Angular velocity, moment of inertia, torque, angular momentum, rolling.

SHM and resonance

Springs and pendulums, energy swap, damping, driving, and resonance.

Electrostatics

Coulomb force, electric field, potential, and a Gauss-law sketch.

Magnetostatics

Lorentz force, Biot–Savart, Ampère, and the solenoid.