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

(a)(1/2)MR^{2}ω

(b)MR^{2}ω

(c)(3/2)MR^{2}ω

(d)2MR^{2} ω

Ans:(c)

Sol: Angular Momentum about Origin O = Angular Momentum about centre of Mass + Angular Momentum of COM about origin

$\large L_o = I\omega + M R v$

$\large L_o = (\frac{MR^2}{2})\omega + M R (\omega R)$

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