The angular acceleration of a body, moving along the circumference of a circle, is :

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

$A$ particle starting from rest moves along the circumference of a circle of radius $r$ with constant angular acceleration $\alpha$. The magnitude of the average velocity,in the time it completes a small angular displacement $\theta$,is:

$A$ wheel is at rest. Its angular velocity increases uniformly and becomes $60 \ rad/sec$ after $5 \ sec$. The total angular displacement is ........ $rad$.

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