Asymmetrical Gravity Center
Name: K. M.
How is center of gravity determined in an asymmetrical object?
As you may have suspected, the center of gravity in an asymmetrical object
may not lie within the object itself. To illustrate this (in two
dimensions): Cut out an irregular shaped (asymmetrical) shape from a piece
of cardboard. Tie a piece of string (that is longer than the maximum size of
the object) to a push-pin. Hang a small weight on the other end of the
string. Stick the push pin through the object near its edge and fasten it to
a vertical surface so that the object is hanging freely and the string is
hanging straight down across the object. Draw a line on the object along the
path of the string. Move the pin to another place on the object near its
edge and repeat the line drawing step. Repeat the process as many times as
You will discover that all the lines cross at the same place -- that's the
object's centroid. If you were to attempt to place the object on a pin at
its centroid, it should balance there.
Now make an object of cardboard that's shaped like a boomerang -- sorta V-
shaped. Repeat the string operation mentioned above and you'll note that the
lines will not cross anywhere on the cardboard. This means that the center of
mass does not reside within the object.
Though it is a bit more complicated, the process works the same for three
dimensional object. For 3-D objects one must use an imaginary cutting plane
rather than a line as was represented by the string.
Probably the easiest way is to suspend the object from two different
points on its surface. The center of mass will always be somewhere on
a vertical line that passes through the point by which the object is
suspended. Once you have determined two such lines, the center of mass
can only be at their intersection.
The center of gravity in all objects is determined by gravity pulling on
each molecule separately. In a solid object, these molecules then push or
pull on their neighbors to keep the object together. The position of the
center of gravity can be thought of as an effect of the sum of all these
pulls. If you let an object hang by a string, the center of gravity will be
hanging straight downward from that string. If you attach the string to
another location, the same center of gravity will still be straight down
from the string. If this did not happen, I do not believe scientists and
engineers ever would have created a center of gravity.
To determine where the center of gravity is mathematically, for an
asymmetric object, requires a form of mathematics called calculus: the math
of tiny changes and tiny pieces. It also requires knowledge of vectors.
Without a great deal of symmetry, even this method is impossible. Unless
you have the same material throughout an object and a great deal of
symmetry, the string method is best.
Dr. Ken Mellendorf
Illinois Central College
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Update: June 2012