A holiday ornament in the shape of a hollow sphere with mass 1.0 Times 10^-2 kg

Question

A holiday ornament in the shape of a hollow sphere with mass 1.0 Times 10^-2 kg and radius 4.5 Times 10^-2 m is hung from a tree limb by a small loop of wire attached to the surface of the sphere. If the ornament is displaced a small distance and released, it swings back and forth as a physical pendulum. Calculate its period. (You can ignore friction at the pivot. The moment of inertia of the sphere about the pivot at the tree limb is 5MR^2/3.) Take the free fall acceleration to be 9.80 m/s^2. Express your answer using two significant figures.

Explanation / Answer

I = (5/3)mr² = 3.375*10^-5

T = 2(I/mgL) = 2*(3.375*10^-5/(0.01*9.81*4.5*10^-2)) = 0.549 sec

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