Physics Formula Sheet

Core mechanics, gravitation, E&M, thermodynamics, waves & optics, and modern physics.

Mechanics

Kinematics (motion)

v = v₀ + a t

x = x₀ + v₀ t + ½ a t²

v² = v₀² + 2 a (x − x₀)

v_avg = (v₀ + v) / 2

Forces

F = m a

F_gravity = m g

F_spring = −k x

Work, energy, power

W = F d cos(θ)

K = ½ m v²

U_g = m g h

U_s = ½ k x²

P = W / t = F v

Momentum

p = m v

F = Δp / Δt

Elastic collision: momentum and kinetic energy conserved.
Inelastic collision: momentum conserved (kinetic energy not necessarily).

Gravitation

F = G m₁ m₂ / r²

g = G M / r²

v_orbit = √(G M / r)

T = 2π √(r³ / (G M))

Electricity & Magnetism

Electrostatics

F = k q₁ q₂ / r²

E = F / q

V = k q / r

Circuits

V = I R

P = I V = I² R = V² / R

Q = C V

U_capacitor = ½ C V²

Magnetism

F = q v B sin(θ)

F = I L B sin(θ)

Φ = B A cos(θ)

ℰ = − dΦ / dt

Thermodynamics

ΔU = Q − W

P V = n R T

K_avg = 3/2 k_B T

Q = m c ΔT

Waves & Optics

v = f λ

n₁ sin(θ₁) = n₂ sin(θ₂)

1/f = 1/d_o + 1/d_i

m = − d_i / d_o

Modern Physics

E = m c²

E_photon = h f

λ = h / p

Δx Δp ≥ ħ / 2