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Center of Inertia, Center of Mass

— geometrical point characterizing the distribution of mass in the mechanical system. The radius vector C.of i. system consisting of $n$ material points, equal $$ \vec{r}_{c i }=\frac{\sum_{i=1}^{n} m_{i} \vec{r}_{i}}{\sum_{i=1}^{n} m_{i}} $$ where $m_{i}$ and $\vec{r}_{i}$ — mass and radius vector of $i$ -th point, and $\sum_{i=1}^{n} m_{i}=M$ — the mass of the system. When moving body (system) his C.of i. moves as a material point with a mass equal to the mass of the entire body, which applied all the forces acting on the body.