Question

Two particles A and B are moving on different concentric circles with different velocities $v_A$ and $v_B$ then angular velocity of B relative to A as observed by A is given by :

• A. $\frac{v_B-v_A}{r_B-r_A}$
• B. $\frac{v_A}{r_A}$
• C. $\frac{v_A-v_B}{r_A-r_B}$
• D. $\frac{v_B+v_A}{r_B+r_A}$

Answer 1

The correct option is A $\frac{v_B-v_A}{r_B-r_A}$

Assuming the particles to be the closest, relative velocity
$v_r=|\overline{v_B}-\overline{v_A}|=v_B-v_A$
and the relative position vector,
$r_r=|\overline{r_B}-\overline{r_A}|=r_B-r_A$
Using $\omega =\frac{v}{r}$, we get relative angular velocity
$\omega =\frac{v_r}{r_r}=,\frac{v_B-v_A}{r_B-r_A}$