What is the angular velocity of the Earth?

$A$ body is moving in a circular path with a constant speed. It has

$A$ particle revolves around a circular path. The acceleration of the particle is

Write the equation for centripetal acceleration in uniform circular motion. Obtain these equations in terms of angular velocity $(\omega)$ and frequency $(\nu)$.

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 $^\circ$)

If the speed $(v)$ and radius $(r)$ of a particle performing uniform circular motion are both doubled,find its new centripetal acceleration.