AP 1 Units & Formulas

Displacement (x) - SI unit

meter (m)

Displacement (x) - Base units

m

Mass (m) - SI unit

kilogram (kg)

Mass (m) - Base units

kg

Time or Period (t or T) - SI unit

second (s)

Time or Period (t or T) - Base units

s

Velocity (v) - SI unit

meter per second (m/s)

Velocity (v) - Base units

m/s

Acceleration (a) - SI unit

meter per second squared (m/s²)

Acceleration (a) - Base units

m/s²

Force (F) - SI unit

Newton (N) = 1 kg•m/s²

Force (F) - Base units

kg·m/s²

Coefficient of Friction (μ) - SI unit

Unitless

Momentum (p) - SI unit

kilogram meter per second (kg·m/s) or Newton second (Ns)

Momentum (p) - Base units

kg·m/s

Impulse (J) - SI unit

kilogram meter per second (kg·m/s) or Newton second (Ns)

Impulse (J) - Base units

kg·m/s

Energy (K, U, W, etc.) - SI unit

Joule (J) = 1 Nm = 1 kg·m²/s²

Energy (K, U, W, etc.) - Base units

kg·m²/s²

Spring Constant (k) - SI unit

Newton per meter (N/m) = kg/s²

Spring Constant (k) - Base units

N/m

Power (P) - SI unit

Watt (W) = 1 J/s = 1 kg·m²/s³

Power (P) - Base units

kg·m²/s³

Angular Displacement (θ) - SI unit

radians (rads)

Angular Displacement (θ) - Base units

rads

Angular Speed or Frequency (ω) - SI unit

radians per second (rad/s)

Angular Speed or Frequency (ω) - Base units

rad/s

Angular Acceleration (α) - SI unit

radians per second squared (rad/s²)

Angular Acceleration (α) - Base units

rad/s²

Rotational Inertia (I) - SI unit

kilogram meter squared (kg·m²)

Rotational Inertia (I) - Base units

kg·m²

Angular Momentum (L) - SI unit

kilogram meter squared per second (kg·m²/s)

Angular Momentum (L) - Base units

kg·m²/s

Torque (τ) - SI unit

Newton meter (Nm) = kg·m²/s²

Torque (τ) - Base units

Nm

Frequency (f) - SI unit

Hertz (Hz) = 1/s

Frequency (f) - Base units

1/s

Volume (V) - SI unit

cubic meter (m³)

Volume (V) - Base units

m³

Area (A) - SI unit

square meter (m²)

Area (A) - Base units

m²

Density (ρ) - SI unit

kilograms per cubic meter (kg/m³)

Density (ρ) - Base units

kg/m³

Pressure (P) - SI unit

Pascal (Pa) = N/m²

Pressure (P) - Base units

N/m²

Volume Flow Rate (Q) - SI unit

cubic meter per second (m³/s)

Volume Flow Rate (Q) - Base units

m³/s

Newton’s Second Law - Equation

F = ma

Force of Friction - Equation

F_friction = μN

Gravitational Force - Equation

F_gravity = G(m₁m₂/r²)

Work - Equation

W = Fd cos(θ)

Power - Equation

P = W/t

Kinetic Energy (translational and rotational) - Equation

KE = ½ mv² (translational), KE = ½ Iω² (rotational)

Potential Energy (gravitational and elastic) - Equation

PE_gravitational = mgh; PE_elastic = ½ kx²

Total Mechanical Energy - Equation

E_total = KE + PE

Work-Energy Theorem - Equation

W = ΔKE

Conservation of Energy - Equation

E_initial = E_final

Impulse-Momentum Theorem - Equation

J = Δp

Conservation of Momentum - Equation

p_initial = p_final

Moment of Inertia for a Point Mass - Equation

I = mr²

Individual Torque - Equation

τ = rFsin(θ)

Newton’s Second Law for Rotation - Equation

τ = Iα

Conservation of Angular Momentum - Equation

L_initial = L_final

Hooke’s Law - Equation

F_spring = -kx

Period of a Spring and Pendulum - Equation

For spring: T = 2π√(m/k); for pendulum: T = 2π√(L/g)

General Wave Function - Equation

y(x, t) = A sin(kx - ωt)

Max Velocity and Acceleration of SHM - Equation

v_max = ωA; a_max = ω²A

Pressure - Equation

P = F/A

Pascal’s Principle - Equation

P₁ = P₂

Bernoulli’s Equation - Equation

P + ½ ρv² + ρgh = constant

Continuity Equation - Equation

A₁v₁ = A₂v₂

Buoyant Force - Equation

B = ρVg

Volume Flow Rate - Equation

Q = A v