$A$ grinding wheel attains a velocity of $20 \ rad/s$ in $5 \ s$ starting from rest. Find the number of revolutions made by the wheel.

As part of maintenance,a jet engine compressor is rotated as shown in the graph. What is the total number of revolutions made by the compressor during the given time interval?

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

The angle turned by a body undergoing circular motion depends on time as $\theta = \theta_0 + \theta_1 t + \theta_2 t^2$. Then the angular acceleration of the body is

If the equation for the displacement of a particle moving on a circular path is given as $\theta = 2t^3 + 0.5$,where $\theta$ is in radians and $t$ is in seconds,then the angular velocity of the particle after $2$ seconds will be ....... $rad/sec$.

$A$ ball is spun with angular acceleration $\alpha = 6t^2 - 2t$,where $t$ is in seconds and $\alpha$ is in $rad/s^2$. At $t = 0$,the ball has an angular velocity of $10 \ rad/s$ and an angular position of $4 \ rad$. The most appropriate expression for the angular position of the ball is: