The moment of inertia of a wheel rotating about an axis is $3 \times 10^2 \ kg \ m^2$ and it has a constant angular speed of $4.6 \ rad \ s^{-1}$. If a retarding torque of $6.9 \times 10^2 \ N \ m$ is applied to the wheel,in how many seconds will the wheel come to rest?

$A$ rod of mass $M$ and length $L$ is placed in a horizontal plane with one end hinged about a vertical axis. $A$ horizontal force of $F = \frac{Mg}{2}$ is applied at a distance $\frac{5L}{6}$ from the hinged end. The angular acceleration of the rod will be:

$A$ 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 $t$?

$A$ pulley of radius $2 \ m$ is rotated about its axis by a force $F = (20t - 5t^2) \ N$ (where $t$ is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is $10 \ kg \cdot m^2$,the number of rotations made by the pulley before its direction of motion is reversed is:

The grinding stone of a flour mill is rotating at $600 \, rad/s$. For this, a power of $1.2 \, kW$ is used. The effective torque on the stone in $N-m$ will be:

The engine of a motor vehicle develops a power of $100 \, kW$. If it rotates at a speed of $1800 \, rpm$,the torque exerted by it is ...... $N-m$.