Moment of inertia of a body about an axis is $4 \,kg-m^2$. The body is initially at rest and a torque of $8 \,N-m$ starts acting on it along the same axis. Work done by the torque in $20 \,s$, in joules, is

$A$ disc is rotating with an angular velocity $\omega_0$. $A$ constant retarding torque is applied on it to stop the disc. The angular velocity becomes $\frac{\omega_0}{2}$ after $n$ rotations. How many more rotations will it make before coming to rest?

One end of a rod is hinged at $O$. The other end is suspended by a string attached to the ceiling as shown in the figure. If the string is suddenly cut,find the angular acceleration of the rod.

Obtain $\tau = I\alpha$ from the angular momentum of a rigid body.

$A$ rope is wound around a hollow cylinder of mass $3\, kg$ and radius $40\, cm.$ What is the angular acceleration (in $rad/s^2$) of the cylinder if the rope is pulled with a force of $30\, N$?

If $I, \alpha$ and $\tau$ are the moment of inertia,angular acceleration,and torque respectively of a body rotating about an axis with angular velocity $\omega$,then: