Two particles $A, B$ are moving on two concentric circles of radii $R_1$ and $R_2$ with equal angula

Question

Two particles $A, B$ are moving on two concentric circles of radii $R_1$ and $R_2$ with equal angular speed $\omega$. At $t=0$, their positions and direction of motion are shown in the figure. The relative velocity $\vec{v}_A-\vec{v}_B$ at $t=\frac{\pi}{2 \omega}$ is given by

Professor PC Thomas Classes · Answer

(c) : The angle transversed in time $\frac{\pi}{2 \omega}$ is \ $ \begin{aligned} & 	heta=\omega t=\frac{\omega \pi}{2 \omega}=\frac{\pi}{2} \ & 	ext { i.e., at } t=\frac{\pi}{2 \omega} \end{aligned} \ $ the position of two particles is shown in the figure. $	herefore \quad$ The relative velocity $\vec{v}_A-\vec{v}_B$ is \ $ =-R_1 \omega \hat{i}-\left(-R_2 \omega \hat{i}ight)=\omega\left(R_2-R_1ight) \hat{i} $