# 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

(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

$L = M v R + I \omega$

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

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

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