Computing the center of mass of an extended object

What if we need to find the center of mass of a complex object -- one which has a continuous distribution of material?

There is a technique we can use: integrate the contribution to the center of mass of each little bit of the object. Let's see how that works by starting with a very simple example and working our way to more complicated ones.

• The center of mass of a ruler (I)
• The center of mass of a ruler (II)
• The center of mass when density varies (I)
• The center of mass when density varies (II)
• The center of mass of a uniform triangle
• The center of mass of a uniform pyramid

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