Two objects of masses m_1 and m_2 are moving | vedclass

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(D) The angular speed $\omega$ is defined as the angle covered per unit time. Since both objects complete one revolution ($2\pi$ radians) in the same

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$r_2 : r_1$

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(D) The angular speed $\omega$ is defined as the angle covered per unit time. Since both objects complete one revolution ($2\pi$ radians) in the same time $t$,their angular speeds are equal: $\omega_1 = \omega_2 = \frac{2\pi}{t}$.Linear speed $v$ is related to angular speed $\omega$ and radius $r$ by the formula $v = r\omega$.For the first object: $v_1 = r_1\omega_1$.For the second object: $v_2 = r_2\omega_2$.The ratio of the linear speed of $m_2$ to that of $m_1$ is $\frac{v_2}{v_1} = \frac{r_2\omega_2}{r_1\omega_1}$.Since $\omega_1 = \omega_2$,the ratio simplifies to $\frac{v_2}{v_1} = \frac{r_2}{r_1}$.

Two objects of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectively. Their respective angular speeds $\omega_1$ and $\omega_2$ are such that they both complete one revolution in the same time $t$. The ratio of the linear speed of $m_2$ to that of $m_1$ is:

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