Q: Two points P and Q, diametrically opposite on a disc of radius R have linear velocities v and 2v as shown in figure. Find the angular speed of the disc.
(a) $\displaystyle \frac{2v}{R} $
(b) $\displaystyle \frac{v}{R} $
(c) $\displaystyle \frac{v}{3R} $
(d) $ \displaystyle \frac{v}{2R} $
Ans: (d)
$ \displaystyle v_{cm} – \omega R = v $ …(i)
$ \displaystyle v_{cm} + \omega R = 2v $ …(ii)
From (ii)-(i)
$ \displaystyle 2\omega R = v $
$ \displaystyle \omega = \frac{v}{2R} $