As a part of a maintenance inspection,the compressor of a jet engine is made to spin according to the graph shown. The number of revolutions made by the compressor during the test is:

$A$ car is moving at a speed of $72 \, km/h$. The diameter of its wheels is $0.25 \, m$. If the wheels stop after completing $20$ revolutions upon applying brakes,the angular retardation produced by the brakes is ....... $rad/s^2$. (in $.5$)

$A$ wheel of radius $0.20 \ m$ starts from rest and rotates with an angular acceleration of $1 \ rad/s^2$. What will be the centripetal acceleration of a point on its circumference when it has rotated through an angle of $90^o$?

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

$A$ particle is moving with constant angular acceleration $4 \text{ rad/s}^2$ in a circular path. At what time will the magnitudes of its tangential acceleration and centripetal acceleration be equal (in $\text{ s}$)?

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?