$A$ torque of $30 \, N \cdot m$ is applied for $10 \, s$ on a wheel of mass $5 \, kg$ and moment of inertia $2 \, kg \cdot m^2$. The angular displacement of the wheel in $10 \, s$ will be ....... radians.

The moment of inertia of a wheel about an axis passing through its center is $200 \, kg \cdot m^2$. $A$ constant torque of $1000 \, N \cdot m$ is applied to rotate the wheel. After $3 \, s$,the angular velocity of the wheel will be ........ $rad/s$.

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

$A$ rope of negligible mass is wound round a hollow cylinder of mass $3 \, kg$ and radius $40 \, cm$. If the rope is pulled with a force of $30 \, N$,then the angular acceleration produced in the cylinder is ........ $rad \, s^{-2}$.

$A$ disc of radius $0.4$ m and mass $1$ kg rotates about an axis passing through its centre and perpendicular to its plane. The angular acceleration is $10$ rad/s$^2$. The tangential force applied to the rim of the disc is (in $N$)

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