Object	Moment of Inertia	Comment
		Since all points of the hoop are equidistant from the axis, this one is easy. See below for the MOI of a disk.
		This is related to the above by the Perpendicular Axis Theorem
		See the derivation below for an annular ring.
		See the derivation below for a rod through its center.
		This is related to the above by the Parallel Axis Theorem
		See the derivation below for a shell.
		See the derivation below for a sphere
		See the derivation below for a slab

Parallel Axis Theorem

This is proven in the text. Suppose the MOI of an object of mass m for an axis passing through its center of mass (cm) is I_cm. Then the moment of inertia for that object about an axis parallel to the original axis and a distance h from the original axis is given by:

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Perpendicular Axis Theorem

Here

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Disk

Here

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Ring

Here

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Rod

Here

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Shell

Here

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Sphere

Here

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Slab

Here