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:

and is measured in rad s-2. In calculus notation, the angular acceleration α is defined by:

\alpha=\lim_{\delta{t}\to 0}\left(\frac{\delta\omega}{\delta{t}}\right)=\frac{d\omega}{dt}

The equation for uniform linear acceleration have rotational analogue which are:

Angular Linear
\omega=\omega_{0}+\alpha{t}
\frac{\theta}{t}=\frac{\omega+\omega_{0}}{2}
\frac{\theta}{t}=\frac{\omega+\omega_{0}}{2}
\omega^2=\omega_{0}^2+2\alpha\theta

where 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 ω (rad) with constant angular acceleration α (rad s-2 in a time interval t(s).