ES-170 Center of Gravity and Centroids for Standard Composite Bodies
If the multitude of forces acting on a body because of the attraction of the earth's gravitational field are replaced by a single force, that force should be applied at the center of gravity (CG).



    
and
    
where
    xCG - x coordinate of C.G.
    yCG - y coordinate of C.G.
    
If we divide the body into n small elements of Wi each, located at xi and yi, then we may write...



If the body is mathematically piecewise continuous, elements may be increased in number and decreased in size...

    
where
    g - specific weight
and
    
If the body is of uniform thickness and specific weight and small enough so that variation in g may be neglected


The centroid (area equivalent of CG) may then be calculated by...

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