Q.An object of mass $m$ has angular acceleration $\alpha = 0.2$ rad s$^{-2}$. What is the angular displacement covered by the object after 3 seconds? (Assume the object started at angle zero with zero angular velocity.)

For circular motion with constant angular acceleration $\alpha$, the linear kinematic equations of straight-line motion translate directly into angular form by the substitutions $s\to\theta$ (angular displacement), $v\to\omega$ (angular velocity), $a\to\alpha$ (angular acceleration), $u\to\omega_0$ (initial angular velocity):

$\omega=\omega_0+\alpha t, \qquad \theta=\omega_0t+\tfrac12\alpha t^2, \qquad \omega^2=\omega_0^2+2\alpha\theta, \qquad \theta=\left(\frac{\omega_0+\omega}{2}\right)t$ …