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,
× 0 + mv
Angular momentum of the system about point Q, LQ
Consider a point R, which is at a distance y
from point Q.
i.e., QR = y
∴ PR = d – y
Angular momentum of the system about point R, LR
) + mv
Comparing equations (i)
, and (iii)
, we getLP
From equation (iv),
we infer that that the angular momentum of a system does not depend on the point about which it is taken.