Question

Two particles A and B are moving as shown in the figure. At this moment of time, the angular speed of A with respect to B is:

• A. $\frac{v_a+v_b}{r}$
• B. $\frac{v_a-v_b}{r}$
• C. $\frac{v_{a}sin\theta -v_{b}sin\theta }{r}$ in anticlockwise direction
• D. $\frac{v_{a}sin\theta +v_{b}sin\theta }{r}$ in anticlockwise direction

Answer 1

Answer: (C)

$\frac{v_{a}sin\theta -v_{b}sin\theta }{r}$ in anticlockwise direction

The angular speed on one particle with respect to other is given by the relative motion of first with respect to the second in direction perpendicular to the line joining them, divided by the distance between them.

Hence $\omega =\frac{v_{a_y}-v_{b_y}}{r}$

$=\frac{v_{a}sin\theta -v_{b}sin\theta }{r}$ in anticlockwise direction.