Two racing cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectively. Their s

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 each makes a complete circle in the same duration of time $t$. The ratio of the angular speed of the first to the second car is:

Accepted Answer

In uniform circular motion, the angular speed $\omega$ is defined as the angle covered per unit time. For a complete revolution (angle $2\pi$), if the time taken is the time period $T$, then the angular speed is given by $\omega = \frac{2\pi}{T}$ .

Given that both cars complete the circle in the same duration of time $t$, their time periods are equal ($T_1 = T_2 = t$).
Therefore, their angular speeds are:
$\omega_1 = \frac{2\pi}{t}$
$\omega_2 = \frac{2\pi}{t}$

The ratio is $\omega_1 : \omega_2 = 1 : 1$. The angular speed is independent of the mass and radius when the time period is fixed.

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