A disc of mass M and radius R is rolling with angular speed on a horizontal plane as shown. The magnitude of angular momentum of the disc about the origin O is

Q: A disc of mass M and radius R is rolling with angular speed on a horizontal plane as shown. The magnitude of angular momentum of the disc about the origin O is

Numerical

(a) $ \frac{1}{2}M R^2 \omega $

(b) $ M R^2 \omega $

(c) $ \frac{3}{2}M R^2 \omega $

(d) $ 2 M R^2 \omega $

Ans: (c)

Sol: Magnitude of Angular Momentum will be

$ L = M v R + I \omega $

$ L = M (\omega R) R + \frac{1}{2}M R^2 \omega $

$ L = M R^2 \omega + \frac{1}{2}M R^2 \omega $

$ L = \frac{3}{2}M R^2 \omega $