In the given figure,the linear acceleration of the solid cylinder of mass $m_2$ is $a_2$. Then,its angular acceleration $\alpha_2$ is (given that there is no slipping):

$A$ thin rod is hinged at point $O$ and is in an unstable equilibrium position. It falls under the influence of gravity due to a slight disturbance. It makes angles of $60^{\circ}$,$90^{\circ}$,and $180^{\circ}$ with the vertical in positions $(2)$,$(3)$,and $(4)$ respectively. If $\omega_2$,$\omega_3$,and $\omega_4$ are the angular velocities in these positions,then:

One end of a rod of length $L$ is on a horizontal plane. It is inclined at an angle $\alpha$ to the horizontal plane. When released,its angular velocity after coming to the horizontal plane is:

$A$ uniform cylinder of mass $m$ can rotate freely about its own axis,which is horizontal. $A$ particle of mass $m_0$ hangs from the end of a light string wound around the cylinder,which does not slip over it. When the system is allowed to move,the acceleration of the descending mass will be

$A$ wheel is rotating at $1200 \ rpm$ and is slowed down at a rate of $4 \ rad/s^2$. The number of revolutions it completes before coming to rest is:

In the figure shown,a mass $m$ is attached to a light string which is wrapped around a solid cylinder of mass $M$ and radius $R$. The system starts from rest at $t = 0$. If friction is negligible,what will be the angular velocity at time $t$?