All Problems Laws of Conservation
Problem 1.196
A certain system of particles possesses a totàl momentum \(\mathbf{p}\) and an angular momentum M relative to a point \(O .\) Find its angular momentum \(\mathbf{M}^{\prime}\) relative to a point \(O^{\prime}\) whose position with respect to the point \(O\) is determined by the radius vector \(\mathbf{r}_{0} .\) Find out when the angular momentum of the system of particles does not depend on the choice of the point \(O\).
1.196. \(\mathbf{M}^{\prime}=\mathbf{M}-\left[\mathbf{r}_{0} \mathbf{p}\right]\). In the case when \(\mathbf{p}=0,\) i.e. in the frame of the centre of inertia.