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The Mathematical Mechanic by Mark Levi

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5

CENTER OF MASS: PROOFS AND SOLUTIONS

5.1 Introduction

The concept of the center of mass was used by Archimedes more than 2,400 years ago.1 Much later Euler introduced another mass-related concept, that of the moment of inertia (see section A.9), which in turn suggested some very nice solutions of mathematical problems [BB]. Here I solve several other mathematical problems using the center of mass.

Recall that the center of mass of a body is the body’s point of balance; the body suspended on that point is in equilibrium in any orientation. Full details can be found in the appendix (section A.8).

As an interesting aside, we take it for granted, from childhood, that such a unique point of balance exists. That is, we assume that the point of balance ...

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