The moment of inertia of a wheel about its transverse axis is $2 \ kg \cdot m^2$ and it is rotating at $60 \ rpm$ about that axis. The torque required to stop the wheel in one minute is:

$A$ wheel rotates at $720 \ rpm$ about an axis passing through its center. It is brought to rest by applying a constant torque for $8 \ s$. What is the value of the torque in $Nm$? (Given: $I = \frac{24}{\pi} \ kg \cdot m^2$)

$A$ 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 $(g = 10 \,m \,s^{-2})$.

$A$ disc has mass $M$ and radius $R$. How much tangential force should be applied to the rim of the disc so as to rotate the disc with angular velocity $\omega$ in time $t$?

$A$ thin uniform rod of mass $M$ and length $L$ is pivoted at a height $\frac{L}{3}$ from its lower end as shown in the figure. The rod is allowed to fall from a vertical position and lie horizontally on the table. The angular velocity of this rod when it hits the table top is . . . . . . . ($g$ = gravitational acceleration)

$A$ flywheel gains a speed of $540\ r.p.m.$ in $6\ s$. Its angular acceleration will be