Editing Centroid (section)

=== Plumb line method ===
The centroid of a uniformly dense [[planar lamina]], such as in figure (a) below, may be determined experimentally by using a [[plumbline]] and a pin to find the collocated center of mass of a thin body of uniform density having the same shape.  The body is held by the pin, inserted at a point, off the presumed centroid in such a way that it can freely rotate around the pin; the plumb line is then dropped from the pin (figure b).  The position of the plumbline is traced on the surface, and the procedure is repeated with the pin inserted at any different point (or a number of points) off the centroid of the object. The unique intersection point of these lines will be the centroid (figure c).  Provided that the body is of uniform density, all lines made this way will include the centroid, and all lines will cross at exactly the same place.

{| cellpadding=3
|- valign=center
| [[File:Center gravity 0.svg|147px|center]]
| [[File:Center gravity 1.svg|183px|center]]
| [[File:Center gravity 2.svg|157px|center]]
|-
| align=center | (a)
| align=center | (b)
| align=center | (c)
|}

This method can be extended (in theory) to concave shapes where the centroid may lie outside the shape, and virtually to solids (again, of uniform density), where the centroid may lie within the body. The (virtual) positions of the plumb lines need to be recorded by means other than by drawing them along the shape.