$A$ constant torque of $1000 \; Nm$ turns a wheel of moment of inertia $200 \; kg \cdot m^2$ about an axis through its centre. The wheel is at rest initially. Its angular velocity after $3 \; s$ is

$A$ circular disc of radius $2 \ m$ is rotating at $240 \ rpm$. If a torque is applied to the disc, it slows down at a rate of $\pi \ rad/s^2$. How long will it take to stop? How many revolutions will the disc complete before coming to rest?

$A$ flywheel of moment of inertia $0.4 \, kg \, m^2$ and radius $0.2 \, m$ is free to rotate about a central axis. If a string is wrapped around it and it is pulled with a force of $10 \, N$,then the angular velocity after $4 \, s$ will be ......... $rad \, s^{-1}$.

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.

An automobile engine develops $100 \ kW$ when rotating at a speed of $1800 \ rev/min$. What torque does it deliver in $N-m$?

$A$ 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?