Question

Find the angular momentum of the particle of mass $0.05\text{kg}$, position vector $\overrightarrow{r}=(8\hat{i}+4\hat{j})\text{m}$ and moving with a velocity $2\hat{i}\text{m/s}$ about the origin.

• A. $-0.4\hat{i}{\text{kg-m}}^2/\text{sec}$
• B. $-0.4\hat{k}{\text{kg-m}}^2/\text{sec}$
• C. $0.4\hat{k}{\text{kg-m}}^2/\text{sec}$
• D. $-0.4\hat{j}{\text{kg-m}}^2/\text{sec}$

Answer 1

The correct option is B $-0.4\hat{k}{\text{kg-m}}^2/\text{sec}$

Given mass of the particle, $m=0.05\text{kg}$
Position vector, $\overrightarrow{r}=(\widehat{8i}+4\hat{j})\text{m}$
velocity vector, $\overrightarrow{v}=2\hat{i}\text{m/s}$

Angular momentum is given by,
$\overrightarrow{L}=m(\overrightarrow{r}\times \overrightarrow{v})=0.05\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 8& 4& 0\\ 2& 0& 0\end{array}\right|$
$=0.05(-8\hat{k})$
$\Rightarrow \overrightarrow{L}=-0.4\hat{k}{\text{kg-m}}^2/\text{sec}$