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  4. Two racing cars of masses m1 and m2 are moving in circles of radii r1 and r2 respectively. Their speeds are such that each makes a complete circle in the same time t . The ratio of the angular speeds of the first to the second car is

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Q. 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 time $ t $ . The ratio of the angular speeds of the first to the second car is

AMUAMU 2015

Solution:

We know that
Angular velocity $ = \frac{\text{ Angular diaplacoment}(\theta)}{\text{Time}}$
As both cars complete their circle $(2\pi)$ in equal time
$\omega_1 = \frac{2\pi}{t} \,\,\,....(i)$
$\omega_2 = \frac{2\pi}{t}\,\,\,...(ii)$
From Eqs. $(i)$ and $(ii)$, we get
$\frac{\omega_1}{\omega_2} = \frac{1}{1}$