The center of gravity is also called the center of mass.The center of gravity is the point at which an object can be balanced.
In the photo, a line has been added to show the center of gravity of the system (chairs + the lady). The center of gravity is also the center of mass of the system.
FYI: The center of mass IS NOT a point in which the mass on one side of the point is equal to the mass on the OPPOSITE side. Instead, the center of mass is a point that acts as if all the mass was centered there. If supported at the center of mass, an object can be balanced.
In the diagram, the key and red bar are equal in length and mass.
The key has an obvious unequal distribution of mass, and thus the center of gravity is not in the center as it is for the red bar.
The key and red bar are both balanced on a support (orange triangle) placed under under their centers of gravity (center of mass).
Math Application
The geometric center of a plane figure is called the centroid. If the plane figure is supported at the centroid, the plane figure will balance. This means the following relations are true:
centroid = center of gravity
= center of mass
Discover for Yourself
How to Locate the Centroid of a Plane Figure
1. Using stiff paper, such as the back of a writing tablet, design and cut out a polygon (plane figure with many sides).
2. With a paper hole punch, cut holes on the different sides of the figure.
3. Using a string that can extend across the figure, tie a weight, such as a metal washer, to one end of the string. Tie the opposite end of the string to a push pin.
4. Place the figure against a vertical cork board.
5. Insert the stick pin in one of the hole, and then allow the paper to hang freely. The paper should be free to rotate around the stick pin.
6. The weighted string should hang vertically across the paper shape.
7. Use a marker to trace the a line next to the hanging string.
8. Rotate the paper so that another hole is at the top. Repeat steps 4through 7.
9. Repeat steps 4 through 8 until you have drawn a line from each of the holes across the paper. Where the lines cross is the centroid of the plane figure (its center of gravity, which is its center of mass).
