# 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.Consider a point R, which is at a distance y from point Q, i.e.,

Angular momentum of the system about point P:

LP=mv×0+mv×d=mvd......(i)

Angular momentum of the system about point Q:

LQ=mv×d+mv×0=mvd....(ii)

Angular momentum of the system about point R:

LR=mv×(d−y)+mv×y=mvd....(iii)

Comparing equations **(i)**, **(ii)**, and **(iii)**, we get:

LP=LQ=LR......(iv)

We infer from equation (iv) that the angular momentum of a system does not depend on the point about which it is taken.