The centripetal acceleration of a car following a circular path is:
[tex]a_c = \omega^2 r[/tex]
where [tex]\omega[/tex] 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
[tex]a_{cA} = a_{cB}[/tex]
which becomes
[tex]\omega_A^2 r_A = \omega_B ^2 r_B[/tex]
or
[tex] \frac{\omega_A}{\omega_B} = \sqrt{ \frac{r_B}{r_A} } [/tex]
and by using the radii of the two orbits, [tex]r_A = 49.6 m [/tex] and [tex]r_B = 39.3 m[/tex], we can find the ratio between the two angular speeds:
[tex] \frac{\omega_A}{\omega_B}= \sqrt{ \frac{r_B}{r_A} }= \sqrt{ \frac{39.3 m}{49.6 m} } =0.89 [/tex]
