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Centre of mass of a Rigid Body (or continuous distribution of mass)

Solid body contain so many particles (atoms) that we can treat them as a continuous distribution of matter.

The 'particles' then become differential mass elements dm, the sum become integrals, and the coordinates of the centre of mass are defined as

$x_{com}=\frac{1}{M}\int\limits xdm$ , $y_{com}=\frac{1}{M}\int\limits ydm$

and  $z_{com}=\frac{1}{M}\int\limits zdm$

Where M is the Centre of Mass of the Body.

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