Archimedes, the Center of Gravity, and the First Law of Mechanics: The Law of the Lever

Archimedes, the Center of Gravity, and the First Law of Mechanics: The Law of the Lever deals with the most fundamental aspects of physics. The book describes the main events in the life of Archimedes and the content of his works. It goes on to discuss a large number of experiments relating to the equilibrium of suspended bodies under the influence of Earth's gravitational force. All experiments are clearly described and performed with simple, inexpensive materials. These experiments lead to a clear conceptual definition of the center of gravity of material bodies and illustrate practical procedures for locating it precisely. The conditions of stable, neutral, and unstable equilibrium are analyzed. Many equilibrium toys and games are described and explained. Historical aspects of the concept are presented, together with the theoretical values of center of gravity obtained by Archimedes. The book also explains how to build and calibrate precise balances and levers. Several experiments are performed leading to a mathematical definition of the center of gravity. These experiments are compatible with the law of the lever, the oldest law of mechanics. Consequences of this law and different explanations of it are described at the end of the book, together with an exhaustive analysis of the works of Euclid and Archimedes. Title Page 2 Bibliographic Information 3 Contents 6 Preface to the Second Edition 10 Acknowledgments 12 Part I - Introduction 14 Chapter 1 - The Life of Archimedes 18 Chapter 2 - The Works of Archimedes 28 Part II - The Center of Gravity 42 Chapter 3 - Geometry 44 Chapter 4 - Experimentms and Definition of the Center of Gravity 50 Chapter 5 - Exploring the Properties of the Center of Gravity 104 Chapter 6 - Historical Aspects of the Center of Gravity 124 Part III - Balances, Levers, and the Oldest Law of Mechanics 138 Chapter 7 - Balances and the Measurement of Weight 142 Chapter 8 - The Law of the Lever 170 Chapter 9 - Mathematical Definition of Center of Gravity 186 Explanations of and Deductions from the Law of the Lever 192 Bibliography 220