Question

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

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

Answer 1

Answer: (B)

The angular momentum of the disc about $O$ is

${\vec{L}}_O=m{\vec{r}}_C\times {\vec{v}}_C+I_C\vec{\omega }$
$=m(x\hat{i}+R\hat{j})\times v\hat{i}+\frac{1}{2}m{R}^2\left(\frac{3v}{R}\hat{k}\right)$
$=m(x\hat{i}+R\hat{j})\times v\hat{i}+\frac{1}{2}m{R}^2\left(\frac{3v}{R}\hat{k}\right)mvR(\hat{j}\times \hat{i})+\frac{3}{2}mvR\hat{k}$
$-mvR\hat{k}+\frac{3}{2}mvR\hat{k}=\frac{mvR}{2}\hat{k}$