If a body moving in a circular path maintains a constant speed of $10 \,ms^{-1}$, then which of the following correctly describes the relation between acceleration $(a)$ and radius $(r)$?

$A$ particle moves so that its position vector is given by $\vec{r} = \cos(\omega t) \hat{i} + \sin(\omega t) \hat{j}$,where $\omega$ is a constant. Which of the following is true?

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

Check the only correct statement in the following:

$A$ stone tied to the end of a string $1\,m$ long is whirled in a horizontal circle with a constant speed. If the stone makes $22$ revolutions in $44$ seconds,what is the magnitude and direction of the acceleration of the stone?

$A$ particle is moving in $U.C.M.$ with speed $V$ and radius $R$. The angular acceleration of the particle is