Question

Two particles A and B are moving on two different concentric circles with different velocities v_Aand v_Bthen 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

Answer: (A)

$\frac{v_{B} - v_{A}}{r_{B} - r_{A}}$

Answer 2

Assuming the particles to be the closest, relative velocity

$v_{r} = \left| {\overrightarrow{v}}_{B} - {\overrightarrow{v}}_{A} \right| = v_{B} - v_{A}$

and relative position vector,

$r_{r} = \left| {\overrightarrow{r}}_{B} - {\overrightarrow{r}}_{A} \right| = r_{B} - r_{A}$

Using ω = v/r, we get relative angular velocity.

ω = $\frac{v_{r}}{r_{r}} = \frac{v_{B} - v_{A}}{r_{B} - r_{A}}$