Question

A disc of mass $m$ and radius $R$ moves in the x-y plane as shown in figure. The angular momentum of the disc about the origin $O$ at the instant shown is:

• A. $-\frac{5}{2}m{R}^2\omega \hat{k}$
• B. $\frac{7}{3}m{R}^2\omega \hat{k}$
• C. $-\frac{9}{2}m{R}^2\omega \hat{k}$
• D. $\frac{5}{2}m{R}^2\omega \hat{k}$

Answer 1

The correct option is A $-\frac{5}{2}m{R}^2\omega \hat{k}$

Total angular momentum of object due to translation and rotation=

$m(\overrightarrow{r}\times \overrightarrow{v})+I\overrightarrow{\omega }$

$=m(3R\hat{j}\times v\hat{i})+\frac{1}{2}m{R}^2\omega \hat{k}$

$=-\frac{5}{2}m{R}^2\omega \hat{k}$