Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass :
Show `L=L'+RxxMV`
Where `L'=sumr'_(i)xxP'_(i)` is the angular momentum of the system about the centre of mass with velocities taken relative to the centre of mass. Remember `r'_(i)=r_(i)-R`, rest of the notation is the standard notation used in the chapter. Note L' and `MRxxV` can be said to be angular momenta, respectively, about and of the centre of mass of the system of particles.

Explanation

From eq. (1), we have
`vec(r_(i))=vec(r._(i))+vecR`
`(dvec(r_(i)))/(dt)=(dvec(r._(i)))/(dt)+(dvecR)/(dt)`
`vec(V_(i))=vec(V._(i))+vecV`
`Mvec(V_(i))=Mvec(V_(i))+MvecV`
[`because` multiplying on both sides by M]
`vec(P_(i))=vec(P._(l))=MvecV`
`vec(r_(i))xxvec(P_(i))=vec(r_(i))xxvec(P._(i))+vec(r_(i))xxMvecV`
[`because` multiplying on both sides by `r_(i)`]
`vecL=vecL+vecRxxMvecV`