PROBLEM 9.179 Consider a cube of mass mand side a. (a) Show that the ellipsoid of inertia at the center of the cube is a sphere, and use this property to determine the moment of inertia of the cube with respect to one of its diagonals. (b) Show that the ellipsoid of inertia at one of the corners of the cube is an ellipsoid of revolution, and determine the principal moments of inertia of the cube at that point. SOLUTION (a) At the center of the cube have (using Figure 9.28) ( )22211126xyzIIImaama===+=Now observe that symmetry implies 0xyyzzxIII===Using Equation (9.48), the equation of the ellipsoid of inertia is 1111666maxmaymaz++=or ()222226xyzRma++==Wwhich is the equation of a sphere. Since the ellipsoid of inertia is a sphere, the moment of inertia with respect to any axis OLthrough the center Oof the cube must always be the same
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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.