Problem 1.197

Demonstrate that the angular momentum $\mathbf{M}$ of the system of particles relative to a point $O$ of the reference frame $K$ can be represented as $$\mathbf{M}=\widetilde{\mathbf{M}}+\left[\mathbf{r}_ {c} \mathbf{p}\right]$$ where $\tilde{\mathbf{M}}$ is its proper angular momentum (in the reference frame moving translationally and fixed to the centre of inertia), $\mathrm{r}_ {C}$ is the radius vector of the centre of inertia relative to the point $O, \mathbf{p}$ is the total momentum of the system of particles in the reference frame $K$