$A$ body performing uniform circular motion of radius $R$ has frequency $n$. Its centripetal acceleration is

$A$ particle revolving in a circular path travels the first half of the circumference in $4 \ s$ and the next half in $2 \ s$. What is its average angular velocity?

$A$ particle is moving on a circular path of radius $r$ with uniform speed $v$. The change in velocity when the particle moves from $P$ to $Q$ is $(\angle POQ = 40^\circ)$.

The position vector of a particle is $\vec{r} = (a \cos \omega t)\hat{i} + (a \sin \omega t)\hat{j}$. The velocity of the particle is

Two cars of masses $m_{1}$ and $m_{2}$ are moving in circles of radii $r_{1}$ and $r_{2}$ respectively. Their angular speeds $\omega_{1}$ and $\omega_{2}$ are such that they both complete one revolution in the same time $t$. The ratio of the linear speed of $m_{1}$ to the linear speed of $m_{2}$ is:

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):