A.4.5 (HL)—Angular motion equations

Uniform angular acceleration

When $\alpha$ is constant, use rotational SUVAT:

$$\omega=\omega_0+\alpha t,\quad \theta=\omega_0t+\frac12\alpha t^2,\quad \omega^2=\omega_0^2+2\alpha\theta$$

Choose the equation

List $\theta,\omega_0,\omega,\alpha,t$, convert revolutions to radians, and choose the equation containing the required unknown and known quantities.

Worked example from local Question Bank row 39408

A bar starts from rest and turns through six revolutions with constant $\alpha=0.110\,\mathrm{rad\,s^{-2}}$. Convert $\Delta\theta=6(2\pi)=12\pi\,\mathrm{rad}$, then

$$\omega_f^2=\omega_i^2+2\alpha\Delta\theta=0+2(0.110)(12\pi)$$
$$\omega_f=2.88\,\mathrm{rad\,s^{-1}}\approx2.9\,\mathrm{rad\,s^{-1}}$$

The equation is valid because angular acceleration is constant.

Common trap

Do not use rotational SUVAT when angular acceleration varies, and do not insert degrees or revolutions where radians are required.