Chapter 11, Problem 44P

(III) Show that the total angular momentum $\stackrel{\to }{L}=\Sigma {\stackrel{\to }{r}}_i\times {\stackrel{\to }{p}}_i$ of a system of particles about the origin of an inertial reference frame can be written as the sum of the angular momentum about the CM, ${\stackrel{\to }{L}}^{*}$ (spin angular momentum), plus the angular momentum of the CM about the origin (orbital angular momentum): $\stackrel{\to }{L}={\stackrel{\to }{L}}^{*}+{\stackrel{\to }{r}}_{\text{CM}}\times M{\stackrel{\to }{v}}_{\text{CM}}$. [Hint: See the derivation of Eq. 11–9b.]