Question

The moment of inertia of a solid sphere of mass M and radius R about
a tangential axis is:
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Answer 1

we first we look up the moment of inertia of a solid sphere with radius R about an axis passing through the centroid of the sphere:

Ic=25mR2

I’m going to use the subscript Ic to refer to the centroidal axis.

Use the parallel axis theorem to determine the moment of inertia about any other axis which is parallel to the centroidal axis:

I=Ic+md2

where d = distance from the centroidal axis to the axis of interest.

The axis of interest for your problem is tangent to the surface, ∴ d=R

I=Ic+md2

I=25mR2+mR2

or

I=25mR2+55mR2

or

I=75mR2