Question

The disc of the radius $R$ is confined to roll without slipping at $A$ and $B$. If the plates having the velocities as shown, determine the angular velocity of disc.

Answer 1

Let $v_0$ be tbe linear velocity and ${\omega }_0$ the angular velocity of the disc as shown in figure then,
$v_0-r{\omega }_0=2v....\left(i\right)$

$v_0+r{\omega }_0=-v....\left(ii\right)$
Solving Eqs. (i) and (ii), we have

${\omega }_0=-\frac{3}{2}\frac{v}{r}$
Hence. the angular velocity of disc is $\frac{3}{2}\frac{v}{r}$ anticlockwise