Question

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

Answer 1

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.