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- Homework Statement
- Prove that the center of mass (CM) of a system composed of several parts can be determined by assuming that all the parts are particles located at their (respective) center of mass.

- Homework Equations
- The CM of a system of particles each having masses ##m_i## and position vectors ##\mathbf{r_i}## is given by : ##\mathbf{r_{\text{CM}}} = \frac{\Sigma m_i \mathbf{r_i}}{\Sigma m_i}##

I have known and used this theorem for a long time solving problems ("Calculate the CM of the some given shape"). I took the theorem to be "obvious" and didn't know it could be proved (and that indeed it was a theorem at all).

I can make no attempt at the proof. Any help would be welcome.

I can make no attempt at the proof. Any help would be welcome.