Definition

Angular velocity and acceleration

ω = \frac{d θ}{d t}, α = \frac{d ω}{d t}

Statement

The rate of change of angular position, and the rate of change of angular velocity.

Symbols and units

When it applies

Rotation about a fixed axis.

Derivation

Defined by direct analogy with linear velocity and acceleration, with angle θ in place of position x:

ω = \frac{d θ}{d t}, α = \frac{d ω}{d t}

Worked examples

Angular speed of a spinning wheel

A wheel accelerates from rest at α = 4.0 rad/s² for 3.0 s:

ω = α t = (4.0) (3.0) = 12 rad/s

Watch out for

Because the analogy is exact, every constant-acceleration equation from M1.2 applies unchanged with x → θ, v → ω, a → α.

Connects to