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

$A$ particle starts rotating from rest. Its angular displacement is expressed by the following equation $\theta = 0.025t^2 - 0.1t$,where $\theta$ is in radians and $t$ is in seconds. The angular acceleration of the particle is:

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

$A$ particle starting from rest moves along the circumference of a circle of radius $r$ with constant angular acceleration $\alpha$. The magnitude of the average velocity,in the time it completes a small angular displacement $\theta$,is:

$A$ wheel,initially at rest,is rotated with a uniform angular acceleration. The wheel rotates through an angle ${\theta _1}$ in the first $1 \ s$ and through an additional angle ${\theta _2}$ in the next $1 \ s$. The ratio $\frac{{\theta _2}}{{\theta _1}}$ is

$A$ 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?