Given several compact objects of known mass and position,
you can find the **center of mass** of the group
in the following way:

or, in a more compact notation,

This method will work well as long as the size of each object is much smaller than the distance between the objects.

Example: given the 3 small objects in the picture below,
with masses **A = 5 kg, B = 2 kg, C = 4 kg,**
what is the location of their center of mass?

The Earth sits on the origin, at position **x = 0**.
Where is the center of mass of the Earth/Moon system?
Is it inside or outside the Earth?
(Yes, you may need to look up some information ....)

Joe makes a circle of radius **R** out of sheet metal.
He then cuts out a smaller circle of half the radius, **R/2**,
so that it just touches the edge of the big circle.

Where is the center of mass of the remaining metal?

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.