$A$ wheel is rotating at $600$ rpm about its axis of rotation. When the power is cut off, it comes to rest in half a minute. Its angular retardation expressed in rad/s$^2$ is (retardation is uniform).

$A$ solid sphere of mass $2 \,kg$ and radius $1 \,m$ is free to rotate about an axis passing through its centre. $A$ constant tangential force $F$ is required to rotate the sphere with $10 \,rad/s$ in $2 \,s$ starting from rest. The value of $F$ is . . . . . . (in $\,N$)

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

To maintain a rotor at a uniform angular speed of $100\, rad\, s^{-1}$,an engine needs to transmit a torque of $100\, Nm$. The power of the engine is

If there is a change of angular momentum from $1\,J\cdot s$ to $5\,J\cdot s$ in $5\,s$,then the torque is:

$A$ constant torque acting on a uniform circular wheel changes its angular momentum from $A_0$ to $4 \,A_0$ in $4 \,s$. The magnitude of the torque is