254_Problem CHAPTER 9

254_Problem CHAPTER 9 - PROBLEM 9.175 For the rectangular...

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PROBLEM 9.175 For the rectangular prism shown, determine the values of the ratios b / a and c / a so that the ellipsoid of inertia of the prism is a sphere when computed ( a ) at point A , ( b ) at point B . SOLUTION ( a ) Using Figure 9.28 and the parallel-axis theorem have at point A .. ( ) 22 1 12 x I mb c =+ () 2 11 4 12 2 12 y a I ma c m m a c  + = +   2 4 12 2 12 z a I b m b + = + Now observe that symmetry implies 0 xy yz zx III ′′ = == Using Equation (9.48), the equation of the ellipsoid of inertia is then 222 1 xyz Ix Iy Iz ′′′ + += or ( ) ( ) 2 2 2 1 44 1 12 12 12 c x c y b z + ++ = For the ellipsoid to be a sphere, the coefficients must be equal.
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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.

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