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How to find the center of gravity and the center of mass?
The formula of the center of mass of the mathematical slender rod is ∫∫D xdxdy= the abscissa area of the center of gravity × d.

The centroid of a surface is the geometric center of a cross-sectional figure. Centroid is used for real objects, and centroid is used for abstract geometry. The geometric center or centroid of object X in N-dimensional space is the intersection of all hyperplanes, which divide X into two parts with equal moments. Unofficially speaking, it is the average of all points on X. If the mass distribution of an object is uniform, the center of mass is the center of gravity.

Center of mass is called center of mass for short.

An imaginary point in a material system that is considered as mass concentration. Unlike the center of gravity, the center of mass does not have to be in a system with a gravitational field. It is worth noting that unless the gravity field is uniform, the center of mass and the center of gravity of the same material system are usually not on the same imaginary point.