Question

Two particle 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 angular momentum is taken?

Answer 1

Vector angular momentum of the system about any point P on x₁y₁.

= vector L_P = m vector v x⁰ + m vector v x d = m vector v d

Similarly vector angular momentum about a point Q on x₂y₂.

vector L_Q = m vector v x d + m vector v x 0 = m vector v d

The vector angular momentum about R,

vector L_R = m vector v (x) + m vector v (d - x) = m vector v d

Clearly, vector(L_P = L_Q = L_R)

Hence the vector angular momentum of the given system is same irrespective of the point about which it is taken.