Question

A circular disc of mass $m$ and radius $R$ is set into motion on a horizontal floor with a linear speed $v$ in the forward direction and an angular speed $\omega =\frac{v}{R}$ in the clockwise direction as shown in Figure. Find the magnitude of the total angular momentum of the disc about the bottommost point $O$ of the disc.

• A. $\frac{1}{2}mvR$
• B. $\frac{2}{3}mvR$
• C. $\frac{3}{2}mvR$
• D. $\frac{4}{3}mvR$

Answer 1

The correct option is A $\frac{1}{2}mvR$

Angular momentum about O

$L_0=\overrightarrow{R}\times \left(m\overrightarrow{v}\right)+I\overrightarrow{\omega }$

$=mRv+\frac{m{R}^2}{2}\times \frac{v}{R}$

$=\frac{3}{2}mRv$