What is barycentre or centre of mass?
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For simple rigid objects with uniform density, the center of mass is located at the centroid. For example, the center of mass of a uniform disc shape would be at its center. Sometimes the center of mass doesn't fall anywhere on the object. The center of mass of a ring for example is located at its center, where there isn't any material.
For more complicated shapes, we need a more general mathematical definition of the center of mass : it is the unique position at which the weighted position vectors of all the parts of a system sum up to zero.
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