The best way to think of the center of gravity of an
object (sometimes also called the center of mass) is think of it as
it's balancing point. In other words if you held on to the object at
its center of mass it would not tend to want to tip one way or another
due to gravity pulling on it.
More specifically, we can think
of gravity acting on an object as pulling directly down on the at the
center of mass. Knowing this we can figure out whether an object is in
equilibrium and whether this equilibrium is stable or not.
very simple: Since gravity pulls downward on the center of mass, an
object will always try to orient itself such that the center of mass is
directly below the point of support.
For a simple example,
consider a meter stick. The center of mass is at the center of the
stick. If you attach a string to one end of the stick and let go of the
other end, it will fall down such that the stick ends up vertical, with
the supported end at the top. In this position the center of mass of
the stick is directly below (a distance of 1/2 meter from) the pivot.
stick hanging at rest in this way in equilibrium (i.e. its not moving).
This equilibrium is stable since if we give the stick a small push it
will just return to the bottom where it was before you pushed it...it
likes being there.
Now suppose you balance the meter sick
vertically at the end of your finger. In this case the stick can still
be motionless (if you balance it well), so it is in equilibrium,
however the equilibrium is not stable since if you give it a small push
it will just fall over instead of returning to it's balance point.
SO, if you want an object to be in a stable equilibrium, make sure the center of mass is directly below the pivot!
(republished on 07/11/06)