Two racing cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectivel

Question

Two racing cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectively. Their speeds are such that they experience the same centripetal acceleration. The ratio of the angular speeds of the first to the second car ($\omega_1 : \omega_2$) is

Professor PC Thomas Classes · Answer

(c) : Centripetal acceleration is given by $a_c = \omega^2 r$. \ Given that $a_{c1} = a_{c2}$, we have: \ $\omega_1^2 r_1 = \omega_2^2 r_2$ \ $\frac{\omega_1^2}{\omega_2^2} = \frac{r_2}{r_1} \implies \frac{\omega_1}{\omega_2} = \sqrt{\frac{r_2}{r_1}}$. \ Note that the mass is completely irrelevant to this ratio.