Center of Mass

All objects have mass, which causes earth's gravity to exert a force on them. This force is the object's weight. The weight of an object is typically felt at the points where the object rests upon other objects. For example, if you hold an object with two hands, a portion of its weight is felt on one hand, and the rest is felt on the other.

But every object has a center of mass about which all of its mass is equally balanced. If you knew where the center of mass of a given object was located, then you could balance the object on your finger by holding it under that point.

The real importance of the center of mass is that the force of gravity, and all inertia forces, can be modeled as passing through the center of mass. No matter how unevenly the mass is distributed throughout the object, the total weight of the object can still be described as acting through the center of mass. Once the center of mass has been computed, it simplifies calculations tremendously.

For symmetrical objects that are made of a single material throughout, the center of mass is simply the center of the object. But irregular shapes are more difficult. Virtual Car must compute the center of mass of any body shape that you draw, no matter how irregular it is.

This is done by dividing your shape into many strips. The weight of each strip (based on the density and thickness of the material that you have specified) is then computed, and multipled by its distance from the left corner of the shape. This product is called the weight moment of the strip. This process is repeated for all of the strips. A running total is kept for the combined weight of all strips, and the sum of the weight moments for each strip. After all strips are examined, the center of mass is computed, by dividing the sum of the weight moments by the total weight of all strips. This whole process yields only the x-coordinate of the center of mass!

To get the y-coordinate of the center of mass, the same process has to be performed using horizontal strips, as if the object were turned on its end, and gravity were acting horizontally.

The center of mass is denoted by the symbol .

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