$A$ wheel having a moment of inertia of $4 \,kg \cdot m^2$ about its symmetrical axis rotates at a rate of $240 \,rpm$ about it. The torque required to stop the rotation of the wheel in one minute is ............ $N \cdot m$.

$A$ triangular plate of uniform thickness and density rotates about an axis perpendicular to the plane of the paper. In case $(a)$,the axis passes through point $A$,and in case $(b)$,it passes through point $B$. If an equal force $F$ is applied as shown in the figure,in which case will the angular acceleration be greater?

$A$ wheel with a moment of inertia of $5 \times 10^{-3} \ kg \cdot m^2$ is rotating at a rate of $20 \ rev/s$. The angular deceleration required to bring it to rest in $20 \ s$ is:

$A$ rope is wound round a hollow cylinder of mass $5\,kg$ and radius $0.5\,m.$ What is the angular acceleration (in $rad/s^2$) of the cylinder if the rope is pulled with a force of $20\,N$?

$A$ solid disc has a diameter of $0.5 \ m$ and a mass of $16 \ kg$. What torque must be applied to increase its angular velocity from $0$ to $120 \ rpm$ in $8 \ s$?

$A$ wheel of radius $0.4 \,m$ can rotate freely about its axis as shown in the figure. $A$ string is wrapped over its rim and a mass of $4 \,kg$ is hung. An angular acceleration of $8 \,rad \,s^{-2}$ is produced in it due to the torque. Then,the moment of inertia of the wheel is $(g = 10 \,m \,s^{-2})$.