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Unformatted text preview: .~:-, Moments and Centers of Mass . Many strUctures and mechanical systems behave as if their masses were concentrated at a single point, called the center of mass It is important to know how to locate mis point, and doing so is basically a mathematical enterprise. For the moment we deal with one- and two-dimensional objects. Three- . dimensional objects are best don~ with multiple integrals. Masses Along a Line We develop our mathematical model in stages. The firststage:is to imagine masses mI, m2, and m) on a rigid x-axis supported by a fulcrumat the origin. The resulting system might balance, or it might nol. It depends on how large the masses are and how mey are arranged. Each mass mt exerts a downward force nltg equal to the magnitude of the mass times me acceleration of gravity. Each of these forces has a tendency to turn me axis about the origin, me way you turn a sees:lw.This turning effect, called a torque, is measured by multiplying the force III ,g by the signed distance Xt from me point of application to me origin. Masses to the left of the origin exertfrom me point of application to me origin....
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This note was uploaded on 09/08/2008 for the course EAC 101 taught by Professor Tyler/ralston during the Fall '08 term at University of Louisville.
- Fall '08