The center of mass of a collection of point masses 
at positions 
is the weighted mean
 |
(1)
|
For a continuous body occupying a region 
with density 
, its mass and center of mass are
 |  |  |
(2)
|
 |  |  |
(3)
|
If all the point masses are equal, or if the density of a continuous body is constant, the center of mass coincides with the geometric centroid. Thus the geometric centroid is the uniform-density special case of the center of mass. For a nonuniform density, the two points need not coincide. In a uniform gravitational field, the center of mass also coincides with the center of gravity.
