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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.

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