Question

A racing car completes 5 rounds on a circular track in 2 minutes. Find the radius of the track if the car has uniform centripetal acceleration of ${\pi }^{2}m/s^2$

Answer 1

Angular velocity of the air:

$\omega =\frac{5\times \left(2\pi \right)}{2\times \left(60\right)}=\frac{\pi }{12}rad/sec$

Centripetal acceleration is given by:

$a_c=\pi {\omega }^2$

Where $r$ is the radius

$\therefore$ $a_c=r\times \frac{{\pi }^2}{144}={\pi }^2\Rightarrow r=144m$