Question

A particle is moving with constant speed $v$ along x-axis in positive direction. Find the angular velocity of the particle about the point $(0,b)$. When position of the particle is $(a,0)$

Answer 1

The above figure represents the motion of particle along x-axis.

From above figure,

$r=\sqrt{a^2+b^2}$

Angular velocity,

$\omega =\frac{v_{perp}}{r}$

$\omega =\frac{v\sin \theta }{r}$

$\omega =\left(\frac{v}{r}\right)\left(\frac{b}{r}\right)$

$\omega =\frac{vb}{r}$

$\omega =\frac{vb}{a^2+b^2}$