Rod AB has length L. velocity of end A of the rod has velocity ${\upsilon }_0$ at the given instant.
(a). Which type of motion the rod has?
(b). Find velocity of end B at the given instant.
(C). Find the angular velocity of the rod.

Solution:
(a). The rod has rotational plus translational motion.
(b). Let velocity of end B is $V_B$ is the direction shown in figure.
Components of $V_A$ and $V_B$ along AB and perpendicular to AB are also shown in the same figure.
Rod is a rigid body. so, distance AB should remain constant or the components along AB should be same.
(c).
Perpendicular to AB, components will be
$v_r=\frac{v_0}{2}+\frac{\sqrt{3}{v}_B}{2}$
substituting $v_B=\sqrt{3}{v}_0$ we get $v_r=2v_0$
Now angular velocity of the rod is $\omega =\frac{v_r}{AB}$
or $\omega =\frac{2v_o}{L}$
Rotation of the rod is anticlockwise. Therefore, from right hand rule $\omega$ is perpendicular to paper outwards or in $\odot$ direction.