A holiday ornament in the shape of a hollow sphere with mass 2.0×10 2 kg and rad

Question

A holiday ornament in the shape of a hollow sphere with mass 2.0×102 kg and radius 5.5×102 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.

Part A

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 5MR2/3.)

Take the free fall acceleration to be 9.80 m/s2 . Express your answer using two significant figures.

Explanation / Answer

I = (5/3)mr² = 5/3 * 2*10^-2*5.5^2*10^-4 = 10.083 * 10^ -5 kg m2

T = 2(I/mgL) = 2*(10.083*10^-5/(2*10^-2*9.81*5.5*10^-2)) = 0.5788 sec. = 0.58 seconds

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