Two particles, each of mass m and speed v, travel in opposite directions along parallel lines separated by a distance d. Show that the vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is taken.
Let at a certain instant two particles be at points P and Q, as shown in the following figure.
Angular momentum of the system about point P:
Angular momentum of the system about point Q:
Consider a point R, which is at a distance y from point Q, i.e.,
Angular momentum of the system about point R:
Comparing equations (i), (ii), and (iii), we get:
We infer from equation (iv) that the angular momentum of a system does not depend on the point about which it is taken.