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

$A$ racing car is travelling along a track at a constant speed of $40\ m/s$. $A$ $T.V.$ cameraman is recording the event from a distance of $30\ m$ directly away from the track as shown in the figure. In order to keep the car under view in the position shown,the angular speed with which the camera should be rotated is ........ $rad/s$.

$A$ merry-go-round makes $120$ revolutions per minute. $A$ child sitting on it starts crying,so the merry-go-round is slowed down with a retardation of $2 \ rad \ s^{-2}$. How long will it take for the merry-go-round to come to a stop? How many revolutions will it make before coming to a stop?

$A$ wheel is rotating at $900 \, r.p.m.$ about its axis. When the power is cut-off,it comes to rest in $1 \, minute$. The angular retardation in $rad/s^2$ 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

The angular speed of a flywheel is increased from $600 \text{ rpm}$ to $1200 \text{ rpm}$ in $10 \text{ s}$. The number of revolutions completed by the flywheel during this time is :