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:

The linear speed of the tip of the seconds hand of a wall clock is $1.05 \, cm \, s^{-1}$. The length of the seconds hand is nearly ........ $cm$.

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

$A$ car wheel rotates at $1200$ revolutions per minute. On pressing the accelerator,it rotates at $4500$ revolutions per minute in $10 \ s$. The angular acceleration of the wheel is ...

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