A particle is moving in a circle with constant speed $v.$ If the radius of the circle is $R,$ find the angular velocity of the particle relative to any point $A$ on the perimeter of the circle.

An aeroplane moves with constant velocity $v$ parallel to $x$ -axis at a height $y=h.$ Find the

(a) angular velocity
(b) angular acceleration of the aeroplane relative to $O$ as the function of time $t.$ Assume that at $t=0, x=0.$

Find the angular velocity of $A$ with respect to $B$ in the figure given below:

Two satellites $1$ and $2$ are orbiting with angular velocities $\omega$ and $2\omega$ relative to the centre of earth respectively, in the same plane. If the radii of their orbits are $r$ and $3r$ respectively, find the angular velocity of $1$ relative to $2\left({\overrightarrow{\omega }}_{1,2}\right)$ and angular velocity of $2$ relative to $1\left({\overrightarrow{\omega }}_{2,1}\right).$

Find the time period of the meeting of the minute hand and second hand of a clock.

Two particles $A$ and $B$ move on a circle. Initially, the particle $A$ and $B$ are diagonally opposite to each other. The particle $A$ move with angular velocity $\mathrm{\pi } \mathrm{rad} {\mathrm{s}}^{-1}$, angular acceleration $\frac{\mathrm{\pi }}{2} \mathrm{rad} {\mathrm{s}}^{-2}$ and the particle $B$ moves with constant angular velocity $2\mathrm{\pi } \mathrm{rad} {\mathrm{s}}^{-1}$. Find the time after which both the particles $A$ and $B$ will collide.