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 \(K\)