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Name: K. M.
Status: student
Age: 14
Location: N/A
Country: N/A
Date: 2001-2002

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 like.

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.

ProfHoff 412

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.

Tim Mooney

K. M.,

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
Physics Instructor
Illinois Central College

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