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?

The angular speed of a flywheel moving with uniform angular acceleration changes from $1200\,rpm$ to $3120\,rpm$ in $16\,s$. The angular acceleration in $rad/s^{2}$ is: (in $\pi$)

$A$ 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 $.5$)

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

$A$ wheel is subjected to uniform angular acceleration about its axis. Initially,its angular velocity is zero. In the first $2 \ s$,it rotates through an angle ${\theta _1}$. In the next $2 \ s$,it rotates through an additional angle ${\theta _2}$. The ratio of ${\theta _2}/{\theta _1}$ is:

$A$ particle moves along a circle of radius $r$ with constant tangential acceleration. If the velocity of the particle is $v$ at the end of the second revolution after the motion has started,then the tangential acceleration is