$A$ torque of $30 \ Nm$ is applied for $15 \ s$ on a stationary wheel of mass $5 \ kg$. The moment of inertia of the wheel is $2 \ kg \ m^2$. The angular displacement of the wheel in $10 \ s$ is ....... $rad$.

$A$ wheel of mass $20 \,kg$ and radius $30 \,cm$ is rotating at an angular speed of $80 \,rev/min$ when the motor is turned off. Neglecting the friction at the axis, calculate the force that must be applied tangentially to the wheel to bring it to rest in $5 \,rev$. (in $\pi \,N$)

$A$ uniform disc of mass $5\,g$ and radius $1\,cm$ is fixed to a thin stick $AB$ of negligible mass as shown in the figure. The system is initially at rest. The constant torque,that will make the system rotate about $AB$ at $25$ rotations per second in $5\,s$,is close to:

$A$ wheel with a moment of inertia of $5 \times 10^{-3} \ kg \cdot m^2$ is rotating at a rate of $20 \ rev/s$. The angular deceleration required to bring it to rest in $20 \ s$ is:

$A$ 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 $rad \ s^{-2}$?

$A$ horizontal heavy uniform bar of weight $W$ is supported at its ends by two men. At the instant one of the men lets go of his end of the rod,the force on the other man's hand changes to: