Two particles, each of mass m and speed u, 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.

Two particles, each of mass m and speed u, travel in opposite directio

1.	Two particles, each of mass m and speed u, 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.
Answer» Solution :Angular momentum, L = myr Choose any axis say 'A' Let at any GIVEN time distance between `m_1 & m_2 = L = L_1 + L_2` About the axis 'A' both will ROTATE in same direction See FIG. `therefore` total angular momentum `L = L_1 +L_2 =muL_1 + muL_2 = mu (L_1 +L_2) = MUL` about any new axis say B distance of `m_1` and `m_2` are say `L'_1 " and "L'_2` ltbtgt Total angular momentum ` L= muL'_1 + muL'_2` or ` L = mu(L'_1 + L'_2) = mu L (because L'_1 +L'_2 =L) ` Hence , total angular momentum of the system is always constant .