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2007-11-09 Moments and Centers of Mass

# 2007-11-09 Moments and Centers of Mass - .~ Moments and...

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.~:-, 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 multipleintegrals. Masses Along a Line We developour mathematicalmodel 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 exert

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2007-11-09 Moments and Centers of Mass - .~ Moments and...

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