Question

A particle is moving along a straight line parallel to x-axis with constant velocity. Find angular momentum about the origin in vector form.

Answer 1

Position vector $\overrightarrow{r}=a\hat{i}+b\hat{j}$

Velocity vector $\overrightarrow{v}=v\hat{i}$

Angular momentum $\overrightarrow{L}=m(\overrightarrow{r}-\overrightarrow{v})$

Or $\overrightarrow{L}=m\left[\right(a\hat{i}+b\hat{j})\times v\hat{i}]$

Or $\overrightarrow{L}=m\left[\right(a\hat{i}\times v\hat{i})+(b\hat{j}\times v\overrightarrow{i}\left)\right]$

Or $\overrightarrow{L}=m\left[\right(0)+(-bv\hat{k}\left)\right]=-mbv\hat{k}$