$A$ wheel having a moment of inertia of $5 \times 10^{-3} \ kg \ m^2$ is rotating at a rate of $20 \ rev/s$. The torque required to stop the wheel in $10 \ s$ is $... \times 10^{-2} \ N \ m$. (in $\pi$)

The angular speed of a motor wheel is increased from $1200 rpm$ to $3120 rpm$ in $16 s$. The angular acceleration of the motor wheel is

$A$ torque of $50\, Nm$ acting on a wheel at rest rotates it through $200\, rad$ in $5\, s$. Calculate the angular acceleration produced. ........... $rad\, s^{-2}$.

$A$ solid cylinder of mass $2\; kg$ and radius $4\; cm$ is rotating about its axis at the rate of $3\; rpm$. The torque required to stop after $2\pi$ revolutions is

$A$ 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 ....... $rad/s$.

$A$ disc has mass $M$ and radius $R$. How much tangential force should be applied to the rim of the disc so as to rotate the disc with angular velocity $\omega$ in time $t$?