$A$ particle is revolving in a circular path of radius $25 \, m$ with a constant angular speed of $12 \, rev/min$. The angular acceleration of the particle is .......... $rad/s^2$.

Two bodies $A$ and $B$ rotate about an axis,such that the angle $\theta_A$ (in radians) covered by the first body is proportional to the square of time,and $\theta_B$ (in radians) covered by the second body varies linearly with time. At $t = 0$,$\theta_A = \theta_B = 0$. If $A$ completes its first revolution in $\sqrt{\pi} \ s$ and $B$ needs $4\pi \ s$ to complete half a revolution,then the ratio of their angular velocities $\omega_A : \omega_B$ at $t = 5 \ s$ is:

The angular velocity of a particle is given by $\omega = 1.5t - 3t^2 + 2$. How much time in $sec$ does it take for the angular acceleration to become zero?

$A$ wheel has a speed of $1200$ revolutions per minute and is made to slow down at a rate of $4 \ rad/s^{2}$. The number of revolutions it makes before coming to rest is

$A$ body moves with a constant angular velocity on a circle. What is the magnitude of its angular acceleration?

$A$ particle performing $U.C.M.$ of radius $\pi/2 \text{ m}$ makes $x$ revolutions in time $t$. Its tangential velocity is