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Consider the system of particles shown.The location of the overall center of mass (r_{G}) is equal to the weighted average of the locations of each individual particle's center of mass.

r_{G} = ∑m_{i}r_{i}/m

A rigid body is a collection of infinitesimally small particles as shown in the figure.Therefore, the location of the center of mass of a rigid body is calculated using the integral form of the system of particles equation above.

r_{G} = (1/m)∫r dm