The axis of rotation is touching the surface of the sphere at one point. That is the definition of tangent. Can it be treated as a point particle distance R from the axis?
Sorry, never heard of that. It's not the goal of the assignment to figure out the moment of inertia around the axis tangent to the surface, but it would be a useful tool.
Well look it up, it is not that difficult. It allows you to use the moment of inertia of a sphere (axis through center) to calculate the moment of inertia somewhere else as long as the other axis is parallel to the axis through the center. And finding the moment of inertia with axis through center is in almost every text book and on the internet. http://en.wikipedia.org/wiki/Parallel_axis_theorem
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