Shortened $\mathrm{com}$, the centre-of-mass is the point about which an object naturally rotates (e.g. when falling). There is equal “mass influence” on the rotational motion, meaning equal moment-of-inertia, on either side of the point.

$$\vec r_\mathrm{com}=\frac{\sum m\vec r}{\sum m}$$

$\vec r$ and $m$ are position and and mass of each point in the rotating object.

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