If $I, \alpha$ and $\tau$ are the moment of inertia,angular acceleration,and torque respectively of a body rotating about an axis with angular velocity $\omega$,then:

$A$ ceiling fan rotates about its own axis with some angular velocity. When the fan is switched off,the angular velocity becomes $\left(\frac{1}{4}\right)^{th}$ of the original in time $t$ and $n$ revolutions are made in that time. The number of revolutions made by the fan during the time interval between switch off and rest is (Angular retardation is uniform):

$A$ wheel having a moment of inertia of $2 \, kg \cdot m^2$ about its vertical axis rotates at the rate of $60 \, rpm$ about the axis. The torque required to stop the wheel's rotation in one minute would be

$A$ rod $PQ$ of mass $M$ and length $L$ is hinged at end $P$. The rod is kept horizontal by a massless string tied to point $Q$ as shown in the figure. When the string is cut,the initial angular acceleration of the rod is

$A$ particle of mass $m$ moves in a circular path of radius $r$,under the action of a force which delivers constant power $P$ and increases its speed. The angular acceleration of the particle at time $t$ is proportional to:

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