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 point of time particles P and Q are in some position (exactly collinear, perpendicular to paths) as shown in figure below,
Angular momentum, I = mvr
Where, m = mass of the particle,
v = velocity of the particle,
r = distance from rotating point.
Thus,
Angular momentum about P, IP = mv×0 + mv×d = mvd …..(1)
Angular momentum about Q, IQ = mv×d + mv×0 = mvd …..(2)
If the rotating point is R as shown in figure above,
IR = [mv× (d-y)] + mv×y
= mvd …………(3)
From equations 1, 2 and 3 we can conclude that angular momentum of system doesn’t depend on the point at which it is taken.