$A$ body rotating with an angular speed of $600 \, rpm$ is uniformly accelerated to $1800 \, rpm$ in $10 \, s$. The number of rotations made in the process is ..... .

$A$ particle moves from point $P_1$ to $P_2$ along a circular path with constant speed $v$. If the angle subtended by the arc $P_1P_2$ at the center is $90^{\circ}$,what is the change in velocity?

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

The length of the second's hand in a watch is $1 \, cm$. The change in velocity of its tip in $15 \, seconds$ is:

The angle turned by a body undergoing circular motion depends on time as $\theta = \theta_0 + \theta_1 t + \theta_2 t^2$. Then the angular acceleration of the body is

$A$ body rotating with uniform angular acceleration covers $100 \pi \text{ rad}$ in the first $5 \text{ s}$ after the start. Its angular speed at the end of $5 \text{ s}$ (in $\text{rad/s}$) is .........$\pi$.