![]() ![]() The center of mass is the unique point at the center of a distribution of mass in space that has the property that the weighted position vectors relative to this point sum to zero. Newton's second law is reformulated with respect to the center of mass in Euler's first law. In the Renaissance and Early Modern periods, work by Guido Ubaldi, Francesco Maurolico, Federico Commandino, Evangelista Torricelli, Simon Stevin, Luca Valerio, Jean-Charles de la Faille, Paul Guldin, John Wallis, Christiaan Huygens, Louis Carré, Pierre Varignon, and Alexis Clairaut expanded the concept further. Other ancient mathematicians who contributed to the theory of the center of mass include Hero of Alexandria and Pappus of Alexandria. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes. In his work On Floating Bodies, Archimedes demonstrated that the orientation of a floating object is the one that makes its center of mass as low as possible. Archimedes showed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point-their center of mass. He worked with simplified assumptions about gravity that amount to a uniform field, thus arriving at the mathematical properties of what we now call the center of mass. The concept of center of gravity or weight was studied extensively by the ancient Greek mathematician, physicist, and engineer Archimedes of Syracuse.
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