$A$ constant torque acting on a uniform circular wheel changes its angular momentum from $A_0$ to $4 \,A_0$ in $4 \,s$. The magnitude of the torque is

$A$ rope is wound around a hollow cylinder of mass $3\, kg$ and radius $40\, cm.$ What is the angular acceleration (in $rad/s^2$) of the cylinder if the rope is pulled with a force of $30\, N$?

$A$ slender uniform rod of mass $M$ and length $l$ is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The rod is released from a position where it makes an angle $\theta$ with the vertical. The angular acceleration of the rod when it makes an angle $\theta$ with the vertical is

Two small balls with masses $m$ and $2m$ are attached to both ends of a rigid rod of length $d$ and negligible mass. If the angular momentum of this system is $L$ about an axis $(A)$ passing through its centre of mass and perpendicular to the rod,then the angular velocity of the system about $A$ is:

$A$ constant torque acting on a uniform circular wheel changes its angular momentum from $L_0$ to $4L_0$ in $4 \ s$. The magnitude of this torque is

$A$ 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 $rad/s^2$.