$A$ wheel has a speed of $1200$ revolutions per minute and is made to slow down at a rate of $4 \ rad/s^{2}$. The number of revolutions it makes before coming to rest is

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

$A$ particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_c$ is varying with time $t$ as $a_c = k^2 r t^2$. The power delivered to the particle by the forces acting on it is:

$A$ fan is rotating with an angular speed of $300 \text{ rpm}$. The fan is switched off,and it takes $80 \text{ s}$ to come to rest. Assuming constant angular deceleration,the number of revolutions made by the fan before it comes to rest is:

The relative angular speed of the hour hand and minute hand of a clock is (in $rad/s$):

The relative angular speed of the hour hand and the second hand of a clock is (in $rad/s$):