The moment of inertia about one end is 1 3 m L 2 1 3 m L 2, but the moment of inertia through the center of mass along its length is 1 12 m L 2 1 12 m L 2. This is because the axis of rotation is closer to the center of mass of the system in (b). We see that the moment of inertia is greater in (a) than (b). Using the parallel-axis theorem eases the computation of the moment of inertia of compound objects. I total = I Rod + I Sphere = 1 3 m Rod L 2 + 2 5 m Sphere R 2 + m Sphere R 2 I total = I Rod + I Sphere = 1 3 m Rod L 2 + 2 5 m Sphere R 2 + m Sphere R 2
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