If a particle covers half the circle of radius $R$ with constant speed $v$,then:

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

For a particle in uniform circular motion,the acceleration $\vec{a}$ at any point $P (R, \theta)$ on the circular path of radius $R$ is (when $\theta$ is measured from the positive $x$-axis and $v$ is uniform speed):

In uniform circular motion,

$A$ cyclist starts from the centre $O$ of a circular park of radius $1\, km$ and moves along the path $OPRQO$ as shown in the figure. If he maintains a constant speed of $10\, m/s$,what is his acceleration at point $R$ in magnitude and direction?

$A$ body is moving with a uniform speed of $20 \,m/s$ on a horizontal circle. The change in velocity of the body in half a revolution is