Question

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

• A. $\left(1/2\right)M{R}^2\omega$
• B. $M{R}^2\omega$
• C. $\left(3/2\right)M{R}^2\omega$
• D. $2M{R}^2\omega$

Answer 1

The correct option is C $\left(3/2\right)M{R}^2\omega$

$v=Rw$ (pure rolling)

Angular momentum about origin O, $L_O=MvR+I_{O}w$

$L_O=M\left(Rw\right)R+\frac{1}{2}M{R}^{2}w$

$L_O=\frac{3}{2}M{R}^{2}w$