A particle is moving with constant speed v along the line y = a in positive x -direction. Find magnitude of its angular velocity about orgine when its position makes an angle `theta` with x-axis.

Explanation

Consider the particle is at point P as shown in the figure. We will resolve its velocity into two components v `cos theta`, which is radial and outward from point O and v `sin theta` which is perpendicular component.

Now, `omega = (V_(_|_))/(r )=(V sin theta)/(r )`
where `(a)/(r )= sin theta`
`rArr = (a)/(sin theta)`
`therefore omega = (v sin^(2)theta)/(a)`