$A$ disc of mass $25 \ kg$ and radius $0.2 \ m$ is rotating at $240 \ r.p.m.$ $A$ retarding torque brings it to rest in $20 \ s$. If the torque is due to a force applied tangentially on the rim of the disc,then the magnitude of the force in newton is

$A$ 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 a disc of mass $M$ and radius $R$ rotates with an angular acceleration $a$, the torque acting on the disc is

$A$ thin solid disk of $1 \ kg$ is rotating along its diameter axis at the speed of $1800 \ rpm$. By applying an external torque of $25 \pi \ Nm$ for $40 \ s$,the speed increases to $2100 \ rpm$. The diameter of the disk is . . . . . . $m$.

$A$ body rotating at $20 \ rad/s$ is acted upon by a constant torque providing it a deceleration of $2 \ rad/s^2$. At what time will the body have kinetic energy same as the initial value if the torque continues to act?

$A$ thin uniform rod of mass $m$ and length $L$ is pivoted at one end so that it can rotate in a vertical plane. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle $\theta$ with the vertical is [consider negligible friction at the pivot] ($g=$ acceleration due to gravity).