Question

The angular momentum of the disc which spins with $\vec{\omega}=\frac{3 v}{R} \hat{k}$ and its CM moves with a velocity $\vec{v}=v \hat{i}$ about $O$ will be

• A. $\frac{3 m v R}{2} \hat{k}$
• B. $\frac{m v R}{2} \hat{k}$
• C. $-\frac{3 m v R}{2} \hat{k}$
• D. $-\frac{m v R}{2} \hat{k}$

Answer 1

Answer: (B)

The angular momentum of the disc about $O$ is

$\vec{L}_{O}=m \vec{r}_{C} \times \vec{v}_{C}+I_{C} \vec{\omega}$
$=m(x \hat{i}+R \hat{j}) \times v \hat{i}+\frac{1}{2} m R^{2}\left(\frac{3 v}{R} \hat{k}\right)$
$=m(x \hat{i}+R \hat{j}) \times v \hat{i}+\frac{1}{2} m R^{2}\left(\frac{3 v}{R} \hat{k}\right) m v R(\hat{j} \times \hat{i})+\frac{3}{2} m v R \hat{k}$
$-m v R \hat{k}+\frac{3}{2} m v R \hat{k}=\frac{m v R}{2} \hat{k}$