In the given figure,the linear acceleration of the solid cylinder of mass $m_2$ is $a_2$. If there is no slipping,find its angular acceleration $\alpha_2$.

$A$ uniform solid cylinder of mass $M$ and radius $R$ rotates about a frictionless horizontal axle. Two similar masses $m$ are suspended with the help of two ropes wrapped around the cylinder. If the system is released from rest,then the acceleration of each mass will be

$A$ rigid body is rotating with angular velocity $\omega$ about an axis of rotation. Let $v$ be the linear velocity of a particle which is at a perpendicular distance $r$ from the axis of rotation. Then the relation $v = r \omega$ implies that

$A$ massless string is wrapped around a disc of mass $M$ and radius $R$. Another end is tied to a mass $m$ which is initially at height $h$ from the ground level as shown in the figure. If the mass is released,then its velocity while touching the ground level will be:

Consider two masses with $m_1 > m_2$ connected by a light inextensible string that passes over a pulley of radius $R$ and moment of inertia $I$ about its axis of rotation. The string does not slip on the pulley and the pulley turns without friction. The two masses are released from rest separated by a vertical distance $2h$. When the two masses pass each other,the speed of the masses is proportional to

$A$ wheel starting from rest gains an angular velocity of $10 \ rad/s$ after being uniformly accelerated for $5 \ s$. The total angle through which it has turned is