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) ()22211126xyzIIIm aama===+=Now observe that symmetry implies 0xyyzzxIII===Using Equation (9.48), the equation of the ellipsoid of inertia is 2222221111666maxmaymaz++=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
This is the end of the preview.
access the rest of the document.
As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.
Temple University Fox School of Business ‘17, Course Hero Intern
I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.
University of Pennsylvania ‘17, Course Hero Intern
The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.