$A$ thin ring of radius $R$ is rotated about its center. Then its radius:

$A$ uniformly thick wheel with moment of inertia $I$ and radius $R$ is free to rotate about its centre of mass (see fig). $A$ massless string is wrapped over its rim and two blocks of masses $m_{1}$ and $m_{2}$ $(m_{1} > m_{2})$ are attached to the ends of the string. The system is released from rest. The angular speed of the wheel when $m_{1}$ descends by a distance $h$ is

As shown in the figure,a small wheel is coaxially connected to a larger wheel of double its radius. The system rotates about a common axis. Strings $A$ and $B$ are attached to the wheels such that they do not slip. If $x$ and $y$ are the distances covered by $A$ and $B$ in the same time interval,then:

For a rigid body in rotational motion,if the linear velocity of a particle at a distance of $2 \ cm$ from the fixed axis of rotation is $10 \ cm \ s^{-1}$,what is the angular velocity of a particle at a distance of $4 \ cm$ from the axis of rotation?

What is the value of linear velocity if $\overrightarrow{r} = 3\widehat{i} + 4\widehat{j} + 6\widehat{k}$ and $\overrightarrow{\omega} = -5\widehat{i} + 3\widehat{j} + 5\widehat{k}$?

$A$ wheel starting from rest gains an angular velocity of $10 \ rad/s$ after being uniformly accelerated for $5 \ s$. The total angle through which it has turned is