What is Center of Gravity? – Definition, Equation & Examples

Understand the meaning of the center of gravity (CG) and its effect on the stability of an object. Learn how to calculate the CG of different systems of objects with a series of examples.
Center of Gravity Defined
Have you ever heard someone say that one of the advantages of being short and stocky is that you’re less likely to get knocked over? They might have even mentioned that it’s because the short and stocky person has a lower center of gravity. The center of gravity (CG) of an object is the point at which weight is evenly dispersed and all sides are in balance. A human’s center of gravity can change as he takes on different positions, but in many other objects, it’s a fixed location.
Follow me through a quick experiment. You’ll need the following:
A #2 pencil
A fine edge like a ruler or a credit card
A permanent marker
A ruler (if you don’t have one, you may be able to eyeball it)
Step 1: Attempt to balance the pencil on the edge you have selected.
Balancing the pencil may take some trial and error. The point at which the pencil balances may not be where you first thought. If it begins to tip in one direction, move the pencil back slowly in the opposite direction until it will stay there on its own.
Step 2: Once the pencil is balanced, mark the location of the balancing point with a permanent marker.
Step 3: Measure the distance between the ends of the pencil and the balancing point you have marked. Are the two lengths equal? On my pencil, the length from the eraser to the balancing point was actually 1.25 inches less than the length from the pencil tip to the balancing point. Why would this be the case?
In our experiment, the balancing point was another word for the center of gravity of this pencil. In other words, if we cut the pencil in two at the mark we made in the experiment, the two parts would be equal in weight. However, they are not equal in length. As you may have already figured out, the metal piece that houses the eraser contributes more to the weight of the pencil, so the CG is closer to that side of the pencil.
Keeping Up with that Center
The center of gravity is an important concept in determining the stability of a structure. It’s the reason why a good homeowner will keep the top branches of his trees trimmed. It’s also the reason why a pick-up truck might not be the best vehicle choice for a first time driver. Stability is maximized in objects with a lower center of gravity and a wide base. The taller and more top-heavy an object, the more likely it is to tip over when it is tilted by a force. This figure demonstrates a bus driving on two different grades; the second one is steep enough to cause the center of gravity to fall outside of the base of the vehicle, which will cause it to topple over.
Center of Gravity Equation
The center of gravity of an object is calculated by taking the sum of its moments divided by the overall weight of the object. The moment is the product of the weight and its location as measured from a set point called the origin.
One Dimensional Example
To make more sense of our CG equation, let’s see it applied in a simple one-dimensional example that I like to call the Confused Weightlifter.
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