PROBLEM 9.126 Determine by direct integration the moment of inertia with respect to the zaxis of the semiellipsoid shown assuming that it has a uniform density and a mass m. SOLUTION First note that when 12220: 1xzyba==−12221xyzca−For the element shown ()221xdmyzdxbcdxaρππρ−Then 2201axmdmbcdxa=∫=−∫3201233abc xxabca=−=For the element 3,area4AAIzyπ′=Then 3,mass,area4AAAAdItIdxzyρρ′′Now 2,masszAAdIdIx dm′=+22232114xxbcdx xdxaaρ+−4422423mb
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This note was uploaded on 07/11/2011 for the course EGM 2511 taught by Professor Jenkins during the Spring '08 term at University of Florida.