What is pure translational motion?

Two small balls are fixed at the ends of a light rigid rod of length $L = 0.4 \ m$. The system is released from a height $h = 5 \ m$ with the rod horizontal. The balls collide with the horizontal surface and rebound. The coefficient of restitution between ball $A$ and the ground is $e_A = 0.6$ and that between ball $B$ and the ground is $e_B = 0.4$. Find the angular speed (in $rad/s$) of the rod just after the collision. Take the acceleration due to gravity $g = 10 \ m/s^2$.

In the following figure,a body of mass $m$ is tied at one end of a light string and this string is wrapped around a solid cylinder of mass $M$ and radius $R$. At the moment $t = 0$,the system starts moving. If the friction is negligible,the angular velocity at time $t$ would be

In the given figure,a solid cylinder of mass $m_2$ and radius $R$ is suspended by a string wrapped around it,which passes over a fixed pulley of mass $m_1$ and radius $R$. If the linear acceleration of the solid cylinder is $a_2$ and there is no slipping,what is its angular acceleration $\alpha_2$?

The direction of the angular velocity vector is along which of the following?

$A$ disc of mass $m$ and radius $r$ is free to rotate about its centre as shown in the figure. $A$ string is wrapped over its rim and a block of mass $m$ is attached to the free end of the string. The system is released from rest. The speed of the block as it descends through a height $h$ is: