Two spheres have the same diameter and mass, but one is solid and the other one...

Two spheres have the same diameter and mass, but one is solid and the other one is hollow. Assuming homogeneous densities and putting the origin at the center, calculate the inertia tensor of each sphere.

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Expert Solution

For the solid sphere, note that the off diagonal terms are 0. Because:

And since the sphere is symmetric, the result holds. For the diagonal terms, we do the following:

Thus the tensor reads:

For the hollow sphere, the same argument as above gives us that the off diagonal terms are all 0. For the diagonal terms, we assume that the shell has a small thickness . Then:

Thus the tensor reads:

genius_generous answered 1 year ago

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