PROBLEM 9.177 For the homogeneous circular cylinder shown, of radius aand length L, determine the value of the ration a/Lfor which the ellipsoid of inertia of the cylinder is a sphere when computed (a) at the centroid of the cylinder, (b) at point A. SOLUTION (a) From Figure 9.28 ()222113212xyzImaIImaL===+Now observe that symmetry implies 0xyyzzxIII===Using Equation (9.48), the equation of the ellipsoid of inertia is then ()()22222222221111: 33121212xyzI xI yI zma xmaLymaL++=++++=For the ellipsoid to be a sphere, the coefficients must be equal. Therefore,
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