$A$ particle moves with constant speed $v$ along a circular path of radius $r$ and completes the circle in time $T$. The acceleration of the particle is

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

The angular velocity of a particle rotating in a circular orbit $100$ times per minute is

The angular speed of the seconds needle in a mechanical watch is:

What is uniform circular motion? By using a proper figure,derive the equation for centripetal acceleration $a_c = \frac{v^2}{r}$ for uniform circular motion. Show that its direction is towards the center.

The position vector of a particle is $\vec{r} = a \cos \omega t \hat{i} + a \sin \omega t \hat{j}$. Calculate the angle between its position vector and the velocity vector. $(\cos 0 = 1, \cos 90 = 0, \cos 60 = 0.5, \sin 30 = 0.5, \sin 0 = 0)$ (in $^\circ$)