Average velocity: v = delta x / delta t
Acceleration: a = delta v / delta t
Velocity with constant acceleration: v = v0 + at
Displacement with constant acceleration: x = x0 + v0 t + 1/2 a t^2
Velocity-displacement relation: v^2 = v0^2 + 2a(x - x0)
Free-fall acceleration: g = 9.8 m/s^2 (about)
Newton's second law: F = ma
Weight: W = mg
Friction force: f = mu N
Hooke's law: F = -kx
Centripetal acceleration: a = v^2 / r
Centripetal force: F = mv^2 / r
Universal gravitation: F = G m1 m2 / r^2
Gravitational field near a planet: g = GM / r^2
Orbital speed: v = sqrt(GM / r)
Work: W = F d cos theta
Kinetic energy: KE = 1/2 m v^2
Gravitational potential energy: PE = mgh
Spring potential energy: PE = 1/2 k x^2
Power: P = W / t
Momentum: p = mv
Impulse: J = F delta t = delta p
Torque: tau = r F sin theta
Angular velocity: omega = delta theta / delta t
Rotational kinetic energy: KE = 1/2 I omega^2
Angular momentum: L = I omega
Period and frequency: T = 1/f
Wave speed: v = f lambda
Spring period: T = 2 pi sqrt(m / k)
Pendulum period: T = 2 pi sqrt(L / g)
Pressure: P = F / A
Hydrostatic pressure: P = P0 + rho g h
Buoyant force: F = rho_fluid V g
Continuity equation: A1 v1 = A2 v2
Bernoulli's equation: P + 1/2 rho v^2 + rho g h = constant
Density: rho = m / V
Heat transfer: Q = m c delta T
Heat for phase change: Q = m L
Ideal gas law: PV = nRT
Average kinetic energy of gas: KE = 3/2 k_B T
First law of thermodynamics: delta U = Q - W
Efficiency of a heat engine: e = W / Q_hot
Carnot efficiency: e = 1 - T_cold / T_hot
Coulomb's law: F = k q1 q2 / r^2
Electric field: E = F / q
Electric field of a point charge: E = k q / r^2
Electric potential energy: U = k q1 q2 / r
Electric potential: V = k q / r
Capacitance: C = Q / V
Energy stored in a capacitor: U = 1/2 C V^2
Current: I = delta Q / delta t
Ohm's law: V = IR
Electric power: P = IV = I^2 R = V^2 / R
Resistors in series: R = R1 + R2 + R3
Resistors in parallel: 1/R = 1/R1 + 1/R2 + 1/R3
Magnetic force on a charge: F = q v B sin theta
Magnetic force on a wire: F = I L B sin theta
Magnetic flux: Phi = B A cos theta
Induced emf (Faraday): emf = -N delta Phi / delta t
Snell's law: n1 sin theta1 = n2 sin theta2
Index of refraction: n = c / v
Lens/mirror equation: 1/f = 1/do + 1/di
Magnification: m = -di / do
Photon energy: E = h f
Speed of light: c = 3.00 x 10^8 m/s
Photoelectric effect: KE max = h f - work function
de Broglie wavelength: lambda = h / p
Mass-energy equivalence: E = m c^2
Radioactive decay: N = N0 (1/2)^(t / half-life)
Time dilation: t = t0 / sqrt(1 - v^2/c^2)
Doppler effect (moving source approaching): f' = f v / (v - v_s)
Sound intensity level: beta = 10 log10(I / I0) decibels
Diffraction grating: d sin theta = m lambda
Single-slit minima: a sin theta = m lambda
Escape velocity: v = sqrt(2GM / r)
Kepler's third law: T^2 is proportional to r^3
Projectile range (level ground): R = v0^2 sin(2 theta) / g
Terminal velocity: Reached when drag force equals weight
Conservation of momentum: m1 v1 + m2 v2 = m1 v1' + m2 v2'
Elastic collision: Both momentum and kinetic energy are conserved
Center of mass: x_cm = sum of m x / sum of m
Power in rotation: P = tau omega
Moment of inertia of a point mass: I = m r^2
Moment of inertia, solid disk: I = 1/2 m r^2
Simple harmonic motion position: x = A cos(omega t)
Angular frequency: omega = 2 pi f
Thermal expansion: delta L = alpha L0 delta T
Heat conduction: Q/t = k A delta T / d
Stefan-Boltzmann law: P = e sigma A T^4
Wien's law: lambda_max T = constant
Unit of force: Newton, N = kg m/s^2
Unit of energy: Joule, J = N m
Unit of power: Watt, W = J/s

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