What is the physical quantity represented by the unit $rpm$? Express it in $rad/s$.

$A$ cycle wheel of radius $0.4\ m$ completes one revolution in one second. Then,the acceleration of a point on the rim of the cycle wheel will be:

$A$ particle is moving on a circular path of radius $r$ with uniform speed $v$. What is the displacement of the particle after it has described an angle of $60^{\circ}$?

$A$ particle is moving with constant speed in a circular path. When the particle turns by an angle $90^{\circ}$,the ratio of instantaneous velocity to its average velocity is $\pi : x \sqrt{2}$. The value of $x$ will be $.........$

$A$ particle is performing $U.C.M.$ along the circumference of a circle of diameter $50 \ cm$ with a frequency of $2 \ Hz$. The acceleration of the particle in $m/s^2$ is:

The figure shows a small wheel fixed coaxially on a bigger one of double the radius. The system rotates about the common axis. The strings supporting $A$ and $B$ do not slip on the wheels. If $x$ and $y$ are the distances travelled by $A$ and $B$ in the same time interval,then