Center of Mass

The center of mass (centroid) has many interesting physical and mathematical applications. For any physical or mathematical entity the center of mass is a point which defines the weighted average position of the total mass. This paper, Center of Mass, provides a rigorous definition, establishes some basic properties, and works many examples of calculating the center of mass in various dimensions and applying it in the proofs of more general results. One such result is the Pappus Centroid Theorem. We show an example where this theorem significantly reduces the work in determining the centroid under investigation. We also show the usefulness of the center of mass in gravitational calculations by providing a detailed proof that under constant gravitational acceleration a body acts on an outside body as if its total mass were concentrated at the center of mass. The Table of Contents lists the worked examples and applications included in the paper. Comments and reporting of errors or typos are always appreciated.