Two cars A and B are moving along concentric | vedclass

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Question

(A) 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: $

Vedclass · Accepted Answer

$1: 1$

Vedclass · Answer

(A) 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 taken to complete one full revolution.Since both cars $A$ and $B$ complete their circular paths in the same time,their time periods are equal,i.e.,$T_A = T_B$.Therefore,the ratio of their angular speeds is: $\frac{\omega_A}{\omega_B} = \frac{2\pi / T_A}{2\pi / T_B} = \frac{T_B}{T_A}$.Substituting $T_A = T_B$,we get: $\frac{\omega_A}{\omega_B} = \frac{T_A}{T_A} = 1$.Thus,the ratio of the angular speed of $A$ to $B$ is $1: 1$.

Two cars $A$ and $B$ are moving along concentric circular paths of radii $R_A$ and $R_B$. If both cars complete their respective circular paths in the same time,what is the ratio of the angular speed of $A$ to that of $B$?

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