$A$ wheel is rotating about an axis through its centre at $720$ revolutions per minute. It is acted on by a constant torque opposing its motion for $8$ seconds until it comes to rest. The number of revolutions made by the wheel in the $8$ seconds is:

$A$ thin uniform rod is pivoted at $O$. It rotates in a horizontal plane with a constant angular velocity $\omega$. At $t = 0$,a small insect starts moving from $O$ towards the other end with a constant speed $v$ relative to the rod. It reaches the other end at $t = T$ and stops. The angular velocity $\omega$ of the system remains constant. Which of the following graphs best represents the magnitude of the torque $|\tau|$ at $O$ as a function of time $t$?

The angular speed of a motor wheel is increased from $1200 rpm$ to $3120 rpm$ in $16 s$. The angular acceleration of the motor wheel is

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

$A$ rigid body rotates about a fixed axis with variable angular velocity $\omega(t) = \alpha - \beta t$ at time $t$,where $\alpha$ and $\beta$ are constants. The angle through which it rotates before it comes to rest is

$A$ thin uniform stick of length $l$ and mass $m$ is held horizontally with its end $B$ hinged on the edge of a table. Point $A$ is suddenly released. The acceleration of the centre of mass of the stick at the time of release is: