• angular displacement $\theta$, in radians
• angular velocity $\omega$, in rad/s
• angular acceleration $\alpha$, in rad/s²

Summary of kinematics, for $\alpha=\mbox{const}$ \[ \begin{array}{l} \omega = \omega_0 + \alpha t \\ \overline{\omega} = {1\over2} \, (\omega+\omega_0) \\ \theta = \overline{\omega} \, t = {1\over2} \, (\omega+\omega_0)t \\ \theta = \omega_0t + {1\over2}\alpha t ^2 \end{array} \]

Rolling without slipping $v_t=\omega \, r$, $a_t=\alpha \, r$

• $\omega,\alpha$ - angular velocity and acceleration describe rotation of the whole object
• $v_t, a_t$ - tangential velocity and acceleration describe the motion of one point on the object

Centripetal acceleration for a uniform rotation

• $a_c$ - describes a change in the direction of $\vec{V}$ ($\alpha=0$ means $a_t=0$) \[ a_c = {{V^2}\over r}= \omega^2 r, \qquad \vec{a_c} \> \bot \> \vec{V} \]
• \( \vec{a_c} \) is centripetal, i.e. toward the centre of rotation