Center of Gravity vs. Center of Mass

The acrobat is able to balance on one hand on top of stacked chairs because her center of mass lines up with the center of mass of the chairs which falls within the foundation of the bottom chair.

The photo of one of the Peking Acrobats demonstrates center of mass. I've added the vertical arrows showing how the acrobats center of gravity as well of the center of gravity of the chairs are in line. The photo was taken by (aka Brent)'s photostream

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

photo by Brent)

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).

311413: Science For Every Kid: Geometry Science For Every Kid: GeometryGeometry is the study of shapes. It uses number and symbols to describe the properties of these shapes and the relationships between them. This book explores two different kinds of geometry: plane geometry (the study of two-dimensional figures, and solid geometry (the study of three-dimensional figures).

The activities in this book make learning about geometry FUN!!!