$A$ particle moves with a constant speed $v$ along a circle of radius $R$. What is the change in velocity of the particle as it moves from point $P_1$ to $P_2$?

If ${a_r}$ and ${a_t}$ represent radial and tangential accelerations,the motion of a particle will be uniformly circular if

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 $^\circ$)

The ratio of the angular velocity of the hour hand of a watch to the angular velocity of the rotation of the Earth is:

$A$ man is running with constant speed along a circular path of radius $2 \sqrt 2 \, m$. He completes $1$ round in $10 \, s$. Find the instantaneous speed at $2.5 \, s$.

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