Formula Sheet

Momentum

p = mv

m = mass (kg), v = velocity (m/s)

Newton's Second Law

F = ma

F = force (N), m = mass (kg), a = acceleration (m/s²)

Kinetic Friction

f_k = μ_k · N

μ_k = coeff. of kinetic friction, N = normal force

Centripetal Force

F_c = mv²/r

r = radius of circular path

Work Done

W = F · d · cos θ

θ = angle between force and displacement

Kinetic Energy

KE = ½mv²

m = mass, v = speed

Gravitational PE

PE = mgh

g = 9.8 m/s², h = height

Elastic PE

PE = ½kx²

k = spring constant, x = extension

Power

P = W/t = Fv

W = work, t = time

Torque

τ = rF sin θ

r = lever arm, θ = angle

Rotational KE

KE_rot = ½Iω²

I = moment of inertia, ω = angular velocity

Angular Momentum

L = Iω

Conserved when no external torque

Wave Speed

v = fλ

f = frequency, λ = wavelength

SHM Displacement

x = A cos(ωt + φ)

A = amplitude, ω = angular frequency

SHM Acceleration

a = -ω²x

Always toward equilibrium

Pendulum Period

T = 2π√(L/g)

L = length, g = gravitational accel.

Spring-Mass Period

T = 2π√(m/k)

m = mass, k = spring constant

Doppler Effect

f' = f(v ± v_o)/(v ∓ v_s)

v = wave speed, v_o = observer, v_s = source

Beat Frequency

f_beat = |f₁ - f₂|

Difference of two close frequencies

Coulomb's Law

F = kq₁q₂/r²

k = 8.99 × 10⁹ N·m²/C²

Electric Field

E = kq/r²

E in N/C or V/m

Electric Potential

V = kq/r

V in volts

Capacitance

C = Q/V

C in farads, Q in coulombs

Capacitor Energy

U = ½CV² = Q²/(2C)

Energy stored in capacitor

Ohm's Law

V = IR

V = voltage, I = current, R = resistance

Electrical Power

P = VI = I²R = V²/R

P in watts

Resistivity

R = ρL/A

ρ = resistivity, L = length, A = area

Series Resistance

R_eq = R₁ + R₂ + ...

Resistors in series

Parallel Resistance

1/R_eq = 1/R₁ + 1/R₂ + ...

Resistors in parallel

Faraday's Law

emf = -dΦ_B/dt

Rate of change of magnetic flux

Magnetic Flux

Φ_B = BA cos θ

B = field, A = area, θ = angle

Lorentz Force

F = q(E + v × B)

Force on charge in E and B fields

Mass-Energy

E = mc²

c = 3 × 10⁸ m/s

Photon Energy

E = hf = hc/λ

h = 6.626 × 10⁻³⁴ J·s

de Broglie Wavelength

λ = h/(mv)

Matter wave of particle

Bohr Energy Levels

E_n = -13.6Z²/n² eV

Z = atomic number, n = quantum number

Rydberg Formula

1/λ = R_H(1/n₁² - 1/n₂²)

R_H = 1.097 × 10⁷ m⁻¹

Photoelectric Effect

KE_max = hf - φ

φ = work function

Radioactive Decay

N = N₀e^(-λt)

t₁/₂ = 0.693/λ