36 Center of Gravity

Center of Gravity

You may have heard the term  center of gravity in reference to balance and you might intuitively know that a toddler’s big head raises their center of gravity, which makes them less stable than adults. We already know that the force of gravity is what gives an object weight, but what is the center of gravity? Think about which body part you feel gravity  pulling on. Do you feel it pulling on just your leg, or your arm, or what? Actually, the force of gravity acts on all of your mass in the same way, according to Newton's Universal Law of Gravitation down to every single molecule and atom.  If we break up your body into many many small chunks of equal mass we could calculate the tiny force of gravity on each one. If we add up all those tiny forces we get your total weight. If we average the locations of all those equal tiny forces, the resulting location would be the center of gravity. If we averaged the location of all the equal chunks of mass that would be the center of mass. Everyday objects, like humans, are small enough that gravity acts uniformly on all parts of the object and the center of gravity and the center of mass are essentially the same location. Check out the following video to learn how to experimentally find the center of gravity (mass) of an irregular object.

Reinforcement Exercises

To find the center of mass mathematically we can break the object into small chunks of mass (m_i). Then multiply each chunk of mass by its own distance horizontal distance (x_i) from a reference point. Adding up all the(m_i x_i) values a dividing that result by the total mass of the object will tell us the horizontal distance of the center of mass from the reference point. For an object with only chunks, it would look like this:

(1)   \begin{equation*} x_{com} = \frac{m_1 x_1 +m_2 x_2 + m_3 x_3}{m_1+m_2+m_3} \end{equation*}

Doing the same, but using the vertical distances from the reference point, will tell us the vertical distance between the reference point and the center of mass (y_{com}). For example, if we chose the floor as our vertical reference point, then y_{com} would be the height of the center of mass above the floor.


Being out of balance means that your center of gravity is no longer above your support base (usually the space between your feet). When that happens you either fall down or take a step to widen your support base (regain your balance). The next chapter will examine why those are the only two options you have.

Computer generated graphic of a human skeleton captured from a computer simulation of a person moving. The person is bending at the waist with arms hanging down toward the floor. The center of mass is indicated by a dot slightly outside and in front of the body at waist level.
The center of gravity of an object (blue dot) is the average location of all gravitational forces. This average location does not necessarily have to be on the object. Image Credit: D. Gordon E. Robertson via wikimedia commons


Freely rotating objects tend to rotate around their center of mass. The following video shows a neat demonstration of that phenomenon:




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