$A$ wheel rotates at $720 \ rpm$ about an axis passing through its center. It is brought to rest by applying a constant torque for $8 \ s$. What is the value of the torque in $Nm$? (Given: $I = \frac{24}{\pi} \ kg \cdot m^2$)

$A$ light rope is wound around a hollow cylinder of mass $5\,kg$ and radius $70\,cm$. The rope is pulled with a force of $52.5\,N$. The angular acceleration of the cylinder will be.....$rad\,s^{-2}$.

Obtain $\tau = I\alpha$ from the angular momentum of a rigid body.

Moment of inertia of a body about a given axis is $1.5\, kg\, m^2$. Initially,the body is at rest. In order to produce a rotational kinetic energy of $1200\, J$,an angular acceleration of $20\, rad/s^2$ must be applied about the axis of rotation for a duration of ......... $\sec$.

$A$ stationary horizontal disc is free to rotate about its axis. When a torque is applied on it,its kinetic energy as a function of $\theta,$ where $\theta$ is the angle by which it has rotated,is given as $K\theta^2.$ If its moment of inertia is $I,$ then the angular acceleration of the disc is

$A$ constant torque of $1000 \; Nm$ turns a wheel of moment of inertia $200 \; kg \cdot m^2$ about an axis through its centre. The wheel is at rest initially. Its angular velocity after $3 \; s$ is