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

$A$ flywheel is rotating at a rate of $150 \text{ rev/minute}$. If it slows at a constant retardation of $\pi \text{ rad/s}^2$, then the time required for the wheel to come to rest is (in $\text{ s}$)

$A$ billiard ball is hit by a cue at a point distance $h$ above the centre. It acquires a linear velocity $v_0$. Let $m$ be the mass and $r$ be the radius of the ball. The angular velocity acquired by the ball is

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?

$A$ 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):

If a disc of mass $M$ and radius $R$ rotates with an angular acceleration $a$, the torque acting on the disc is