Moments of Inertia

    In general, a lamina of density covering the region in the first quadrant of the plane has (first) moment about a line given by  



where is the distance from a typical point in to Similarily, the second moment, or the moment of inertia, of about is defined by



In physics, the moment of inertia measures the tendency of the lamina to resist a change in rotational motion about the axis Moments of inertia about the coordinate axes are given by  

Example (Moments of Inertia of a Planar Lamina) Find the moments of inertia and of a homogenuous disk with density center the origin, and radius

    Solution. The boundary of   is the circle and in polar coordinates is described  by We have:









Thus,  

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Moments Of Inertia
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/moments-of-inertia.html