$A$ wheel is subjected to a torque of $1000 \ N-m$ and rotates with a moment of inertia of $200 \ kg-m^2$ about an axis passing through its center. What will be the angular velocity of the wheel after $3 \ s$?

$A$ rectangular plate of mass $20 \ kg$ is suspended from points $A$ and $B$ as shown in the figure. If the pin at $B$ is suddenly removed,find the angular acceleration of the plate in $rad/s^2$.

$A$ pulley of radius $10 \ cm$ has a moment of inertia of $10^{-3} \ kg \ m^2$ about its geometric axis. $A$ time-varying tangential force $F = (0.5t - 0.3t^2) \ N$ is applied to its rim. The pulley is initially at rest. If $t$ is in seconds,what will be the angular acceleration of the pulley at $t = 3 \ s$ in $rad \ s^{-2}$?

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

$A$ 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):

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 ...... $N-m$.