# Angular Acceleration

The angular acceleration α of a rotating body is its rate of change of angular velocity ω. If a small angular velocity change δω change occurs in a small time interval δt, the angular acceleration α is given by:

α = limδt->0(δωδt ) = dωdt

and is measured in rad s-2. The equations for uniform linear acceleration have rotational analogue which are:

Angular Linear
ω = &omega0 + αt
v = v0 + aΔt
(θ/t) = (ω + ω0)/2
<v> = (v + v0)/2
θ = θ0 + ω0t + 1/2 αt2
x = x0 + v0&Deltat + (1/2)aΔt2
&omega2 = ω02 + 2αθ
v2 = v02 + 2a(x - x0)

where <v> is the average velocity, ω0 is the initial angular velocity and ω is the finial velocity (both in rad s-1 after the body has rotated through angular displacement θ (rad) with constant angular acceleration α (rad s-2 in a time interval t(s).