Rotational Kinematics Formulas

Symbol for angular velocity

omega (ω)

Angular velocity (ω) is equal to… (in relation to angle)

ω = ^Δθ/_Δt (angular velocity = angle / time)

Symbol for angular acceleration

alpha (α)

Angular acceleration (α) is equal to… (in relation to angular velocity)

α = ^Δω/_Δt (angular acceleration = change in angular velocity / time)

Angular velocity (ω) is equal to… (in relation to distance)

ω = s/rt (angular velocity = distance / radius * time)

Linear velocity (v) is equal to… (in relation to angular velocity)

v = rω (linear velocity = radius * angular velocity)

Distance traveled on a circle (s) is calculated with the formula…

s = rθ (distance = radius * angle)

Angular displacement (or angle) is calculated with the formula…

θ = s/r (angular displacement = distance / radius)

Angular acceleration (α) is equal to… (in relation to linear velocity)

α = v/rt (angular acceleration = linear velocity / radius * time)

Angular velocity (ω) is equal to… (in relation to linear velocity)

ω = v/r (angular velocity = linear velocity / radius)

Linear acceleration (a) is equal to… (in relation to angular acceleration)

a = αr (linear acceleration = angular acceleration * radius)

Linear acceleration (a) is equal to… (in relation to linear velocity)

a = v/t (linear acceleration = change in linear velocity / time)

Centripetal acceleration is equal to…

a_c = v²/r = rω² (centripetal acceleration = linear velocity squared / radius = radius * angular velocity squared)

Total linear acceleration is…

The vector sum of tangential and centripetal accelerations.

Tangential acceleration is equal to…

a_t = αr = r * (Δω/Δt) (tangential acceleration = angular acceleration * radius = radius * change in angular velocity / change in time)

Total linear acceleration equation is…

a_T = √(a_t² + a_c²)

Angular velocity (ω) is equal to… (in relation to frequency)

2πf (angular velocity = 2 * pi * frequency)

Rotational kinetic energy (KE) is equal to…

KE = ½Iω² (rotational kinetic energy = 1/2 moment of inertia * angular velocity squared)

Angular momentum (p) is equal to…

p = Iω (angular momentum = moment of inertia * angular velocity)

Equation for torque given moment of inertia

Τ = Iα (torque = moment of inertia * angular acceleration)