$A$ particle is moving with a constant speed $v$ in a circle. What is the magnitude of average velocity after half rotation?

If the angular velocity of a merry-go-round is $60^o/s$ and you are $3.5\,m$ from the centre of rotation,your linear velocity will be

Two particles having mass $M$ and $m$ are moving in a circular path with radius $R$ and $r$ respectively. The time period for both the particles is same. The ratio of angular velocity of the first particle to that of the second particle will be

Derive the formula $a_c = R\omega^2$ from $a_c = \frac{v^2}{R}$.

For a particle in uniform circular motion,the acceleration $\vec{a}$ at a point $P(R, \theta)$ on the circle of radius $R$ is (Here $\theta$ is measured from the $x$-axis):

$A$ particle is performing uniform circular motion along the circumference of a circle of diameter $1 \ m$ with a frequency of $4 \ Hz$. The acceleration of the particle in $m/s^2$ is (in $\pi^2$)