$A$ mass of $2 \ kg$ is moving in a circular path of radius $0.8 \ m$ with an angular velocity of $44 \ rad/s$. If the radius of the path becomes $1 \ m$,the new angular velocity will be ........ $rad/s$.

$A$ train is moving slowly at $2 \, m/s$ next to a railway platform. $A$ man,$1.5 \, m$ tall,alights from the train such that his feet are fixed on the ground. Taking him to be a rigid body,the instantaneous angular velocity (in $rad/s$) is

$A$ torque is applied to a body,changing its angular velocity from $\omega_1$ to $\omega_2$. What is the ratio of the initial radius of gyration to the final radius of gyration?

In the above problem,the angular velocity of the system after the particle sticks to it will be ....... $rad/s$. (in $.3$)

$A$ disc of mass $M$ and radius $R$ is rolling with angular speed $\omega$ on a horizontal plane as shown. The magnitude of angular momentum of the disc about the origin $O$ is

$A$ thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega$. Two objects,each of mass $m$,are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity: