(C) The angular speed $\omega$ of an object moving in a circular path is defined as the rate of change of angular displacement,given by the formula $\

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(C) The angular speed $\omega$ of an object moving in a circular path is defined as the rate of change of angular displacement,given by the formula $\omega = \frac{2\pi}{T}$,where $T$ is the time period of one complete revolution.Since both cars complete their respective circles in the same duration of time $T$,their time periods are equal.Therefore,the ratio of their angular speeds is $\frac{\omega_1}{\omega_2} = \frac{2\pi / T}{2\pi / T} = 1:1$.Thus,the correct option is $C$.

Class 11 Physics 3-2.Motion in Plane Angular Variables and Basic of Uniform Circular Motion

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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

AIPMT 1999 All AIPMT

A
$m_1:m_2$
B
$r_1:r_2$
C
$1:1$
D
$m_1r_1:m_2r_2$

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3-2.Motion in Plane

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Angular Variables and Basic of Uniform Circular Motion

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$A$ particle is moving on a circular path of radius $r$ with uniform speed $v$. What is the displacement of the particle after it has described an angle of $60^{\circ}$?

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$A$ particle is moving on a circular path of radius $r$ with uniform speed $v$. The magnitude of change in velocity when the particle moves from $P$ to $Q$ is $(\angle POQ = 40^o)$.

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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

Similar Questions

$A$ particle moves so that its position vector is given by $\vec{r} = \cos(\omega t) \hat{i} + \sin(\omega t) \hat{j}$,where $\omega$ is a constant. Which of the following is true?

$A$ particle performing uniform circular motion of radius $\frac{\pi}{2} \,m$ makes $x$ revolutions in time $t$. Its tangential velocity is

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$A$ particle is moving on a circular path of radius $r$ with uniform speed $v$. What is the displacement of the particle after it has described an angle of $60^{\circ}$?

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