Question

A particle is moving with constant speed in a circle as shown in Fig. Find the angular velocity of the particle $A$ with respect to fixed point $B$ and $C$ if angular velocity with respect to $O$ is $\omega$

Answer 1

Angular velocity of $A$ with respect to $o$ is

${\omega }_{AC}=\frac{\left(v_{AO}\right)\perp }{r_{AO}}=\frac{v}{r}=\omega$

${\omega }_{AB}=\frac{(AB}{r_{AB}\perp }=\frac{v}{2r}=\frac{\omega }{2}$

and ${\omega }_{AC}=\frac{\left(AC\right)\perp }{r_{AC}}=\frac{v}{3r}=\frac{\omega }{3}$