## Question:

Consider the situation depicted in the figure. At the instant shown, how are the angular momenta of particle P with respect to O and Q related?

## Step-by-step

At the instant shown ${ \overrightarrow { h } }_{ O }={ \overrightarrow { h } }_{ Q }$.The reason is that $\left| \overrightarrow { { h }_{ O } } \right| =\left| \overrightarrow { { h }_{ Q } } \right|$  since it is easy to see that

$\left| \overrightarrow { { h }_{ O } } \right| =m{ \upsilon }_{ P }h$ and $\left| \overrightarrow { { h }_{ Q } } \right| =m{ \upsilon }_{ P }h$

where h is the perpendicular distance between the line between line OQ, and the velocity vector ${ \overrightarrow { \upsilon } }_{ P }$ . Since the direction of ${ \overrightarrow { h } }$ is given by the right-hand rule, we see that both ${ \overrightarrow { h } }_{ O }$ and ${ \overrightarrow { h } }_{ Q }$ point into the page and so must be equal.