Answer to Question #82063 in Physics for Saya Nakamura

Question

What is the solution to this moment of inertia problem?
A cube has homogeneous density, "x" weight and the edges lengthes are "y".

Put the cubes moment of inertia in order of magnitude for the following three axis' that passes through the center of mass.
a, The two visavis side( from the center of both sides)
b, the two visavis edge( from the center of both edges)
c, one body diagonal

I hope my question is understandable, english is not my first language. I put a picture to help you to understand more where is the three moment of inertia.
Thank you for the help, Saya Nakamura

Answer 1

Since the cube is symmetrical about all 3 axes that passes through the middles of its opposite faces and it has homogeneous density, its ellipsoid of inertia is given by a sphere. It means that the moments of inertial about all axes that path through its center of mass are the same. Thus a=b=c.