Mechanics 2: Linear and Rotational Dynamics - 3D Math Primer for Graphics and Game Development - page 586

Figure 12.7
Experimentally measuring the center of mass of a odd-shaped piece of particle board

12.3.2 The Center of Mass

Our discussion of momentum has led us to consider the center of mass of
an object. Let's say a few more words concerning this important concept.
For everyday purposes, the center of mass is equivalent to the center of
gravity, which is essentially the point around which the object is perfectly
balanced. If we balance an object on the tip of a very thin rod or hang it
from a wire, then the rod or wire will be in a line that contains the center
of mass.
Before we discuss how to compute the center of mass mathematically,
let's see how we can measure it experimentally. Imagine that we have some
object with an odd shape, or of an irregular density. We can determine
its center of gravity by hanging the object from any arbitrary point on the
surface of the object. This defines a vertical line upon which the center
of gravity must lie. By repeating the experiment with a different point on
the object and finding the intersection of those two lines, we can locate the
center of gravity.
The authors performed this experiment on a piece of particle board,
as shown in Figure 12.7. First, the board was cut into a purposefully
asymmetric shape. Next, we chose three arbitrary locations from which
to hang the board, and when the board had finished swinging around, we
drew a heavy line on it, coincident with the string by which the board
was suspended. Sure enough, physics worked, and the third line passed
right through the intersection of the first two lines, at the board's center of
mass.