An athlete runs along a circular track of diameter $80 \ m$. The distance travelled and the magnitude of displacement of the athlete when he covers $3/4$th of the circle is (in $m$):

What is the linear velocity of a particle in uniform circular motion of radius $A$ and angular velocity $\omega$?

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

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

The figure shows a small wheel fixed coaxially on a bigger one of double the radius. The system rotates about the common axis. The strings supporting $A$ and $B$ do not slip on the wheels. If $x$ and $y$ are the distances travelled by $A$ and $B$ in the same time interval,then

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