[UPSC CSE 1998] Rigid Body Dynamics (Q242, 20M)

Show that the angular momentum of a particle located at position \vec{r} relative to the origin of co-ordinates is given by \vec{l} = \vec{r} \times \vec{p} where \vec{p} is the linear momentum of the particle. Using this result prove that the angular momentum of a system of particles can be expressed as the sum of their angular momentum around the centre of mass and the angular momentum around the origin of a single particle of mass equal to the total mass of the system located at the centre of mass.