Home > Courses > 1P21_Sternin > RotationalMotion Kinematics of rotational motion 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