Centroid formula - 17.2: Centroids of Areas via Integration

Centroid and Center of Mass are the same point for bodies with a uniform density Just as with the centroids of an area, centroids of volumes and the center of mass are useful for a number of situations in the mechanics course sequence, including the analysis of distributed forces, simplifying the analysis of gravity which is itself a distributed force , and as an intermediate step in determining mass moments of inertia.

For example, the figure below a is easily divided into a square and a triangle, both with positive area; and a circular hole, with negative area b.

The area of the triangle is 1.