$A$ 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:

Obtain the relation between angular momentum of a particle and torque acting on it.

$A$ string is wrapped around the rim of a wheel of moment of inertia $0.20\, kg-m^2$ and radius $20\, cm$. The wheel is free to rotate about its axis and initially the wheel is at rest. The string is now pulled by a force of $20\, N$. The angular velocity of the wheel after $5\, s$ will be ....... $rad/s$.

In the following figure,$r_1 = 5 \, cm$ and $r_2 = 30 \, cm$. If the moment of inertia of the wheel is $5100 \, kg \cdot m^2$,then its angular acceleration will be:

$A$ wheel having a moment of inertia of $2 \, kg \cdot m^2$ about its vertical axis rotates at the rate of $60 \, rpm$ about the axis. The torque required to stop the wheel's rotation in one minute would be

$A$ 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 $30\, N$?