Consider the octant of a uniform sphere of density 5 grams per cubic centimeter and radius (a)

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Consider the octant of a uniform sphere of density 5 grams per cubic centimeter and radius \(a\) lying in the first octant.

a. Find the inertia tensor about the origin.

b. What are the principal moments of inertia?

c Find the principal axes of inertia, that is, the eigenvectors of the inertia tensor.

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