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.

Explanation

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 .