A wheel of radius $1 m$ rolls freely with an angular velocity of $5 rad/s$ and with an angular acceleration of $4 rad/s^2$ , both clockwise as shown in Figure. Determine the velocity of points $A$and $B$.

Velocity : Translational velocity of the centre of mass O

$v_0=\omega r=5\times 1=5m/s$

The motion of points $A$ and $B$ maybe looked at as translational of $O$ and rotation about $O$

For point A, 

${\overrightarrow{v}}_A={\overrightarrow{v}}_O+{\overrightarrow{v}}_{AO}$

or $v_A={\overrightarrow{v}}_O+\omega \left(OA\right)=5+5\times 1$

$=10m/s$

For point B, ${\overrightarrow{v}}_B={\overrightarrow{v}}_O+{\overrightarrow{v}}_{BO}$

or $v_B=\sqrt{v_O^2+v_{bO}^2+2v_O{v}_{BO}\cos 30°}$

Here $v_{BO}=\omega \left(OB\right)$

$$\begin{gathered} =5 0.6 3 m/s \\ \therefore v_B=\sqrt{5+3+2\times 5\times 3\times \cos 30°} \\ =7.74 m/s \end{gathered}$$