Question

Two formula one racing cars are negotiating a circular turn, and they have the same centripetal acceleration. however, the path of car a has a radius of 49.6 m, while that of car b is 39.3 m. determine the ratio of the angular speed of car a to the angular speed of car
b.

Answer 1

The centripetal acceleration of a car following a circular path is:
$a_c = \omega^2 r$
where $\omega$ is the angular speed of the car, and r is the radius of the orbit.

The problem says that the centripetal acceleration of car A is equal to that of car B, so we can write
$a_{cA} = a_{cB}$
which becomes
$\omega_A^2 r_A = \omega_B ^2 r_B$
or
$\frac{\omega_A}{\omega_B} = \sqrt{ \frac{r_B}{r_A} }$

and by using the radii of the two orbits, $r_A = 49.6 m$ and $r_B = 39.3 m$, we can find the ratio between the two angular speeds:
$\frac{\omega_A}{\omega_B}= \sqrt{ \frac{r_B}{r_A} }= \sqrt{ \frac{39.3 m}{49.6 m} } =0.89$