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A uniform disk of mass M and radius R has rotational inertia about its central axis of Idisk = 1/2 MR2. A uniform rod of mass m and length R has rotational inertia about its center, perpendicular to its length of Irod = 1/12 mR2. The rod is now glued to the disk so that one end lies at the center of the disk and the other end is at the disk's rim. What is the rotational inertia of the composite object about the central axis of the disk?

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MathPhys

Answer:

5/6 MR²

Explanation:

In the composite object, the distance from the disk's axis to the rod's axis is R/2.  Using parallel axis theorem, the rod's new moment of inertia is:

I = 1/12 MR² + M (R/2)²

I = 1/12 MR² + 1/4 MR²

I = 1/3 MR²

The total moment of inertia is therefore:

I = 1/2 MR² + 1/3 MR²

I = 5/6 MR²