Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass :
Show `(dL')/(dt)=sumr'_(i)xx(dp')/(dt)`
Further. Show that `(dL')/(dt)=tau'_(ext)`
Where `tau'_(ext)` is the sum of all external torques acting on the system about the centre of mass.

Explanation

Use the definition of centre of mass and Newton.s Third Law. Assume the internal forces between any two particles act along the line joining the particles.)
`vecL=vecL.+vecRxxMvecV`
`(dvecL)/(dt)=(d)/(dt)vec(L.)+(d)/(dt)[vecRxxMvecV]`
`tau_("external")=(dvec(L.))/(dt)+vecVxxMvecV`
But `vecVxxMvecV=0`
`therefore tau_("external")=(dvec(L.))/(dt)`