Centripetal acceleration of a cyclist completing $7$ rounds in a minute along a circular track of radius $5 \, m$ with a constant speed,is ......... $m/s^2$.

If $\vec{L}$ and $\vec{P}$ represent the angular momentum and linear momentum respectively of a particle of mass $m$ having position vector $\vec{r} = a(\hat{i} \cos \omega t + \hat{j} \sin \omega t)$,the direction of the force acting on the particle is:

What is the angular velocity of the second hand of a clock?

$A$ motorcyclist going round in a circular track at a constant speed has:

The angular velocity of a flywheel making $120$ revolutions per minute is:

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