Starting with the formula for the moment of inertia of a rod rotated around an axis through one end perpendicular to its length (I=M ℓ² / 3), prove that the moment of inertia of a rod rotated about an axis through its center perpendicular to its length is I=M ℓ² / 12. You will find the graphics in Figure 10.12 useful in visualizing these rotations.