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1. Finding the Moment of Inertia of a Uniform Thin Rod with mass M and length L rotating about its center (a thin rod is a ID object; in the figure the rod has a thickness for clarity): For this problem, use a coordinate axis with its origin at the rods center and let the rod extend along the x axis as shown here (in other problems, you will need to generate the diagram): dx dm Now, we select a small section of the rod (it is important to not pick a special portion like the far left, exact center, or far right to avoid introducing symmetry which does not hold for the entire object). If this section has a differential mass dm, it has differential length dr as shown Draw a bracket (similar to the one showing the rods length and the differential length) to show the differential elements x-coordinate and label it x. How are r (in the definition of moment of inertia) and x related to each other? a. b.
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