For any thin, uniform rod of length L and mass M , the moment of inertia for rot

Question

For any thin, uniform rod of length L and massM, the moment of inertia for rotation about one end

is I = (1/3)ML2. And the moment of inertia ofany object is simply the sum of the moments of inertia

of its parts. Use those two facts to compute the answer to thisquestion: Suppose you have a thin,

uniform rod with a total mass of 3.00 kg and a total length of2.00 m. By what percentage does the

moment of inertia decrease if you rotate it instead about apoint located 20% (0.40 m) in from one

end, as shown?

Explanation / Answer

I = 1/3 M L2 = 1/3 * 3 * 4 = 4kg-m2     moment of inertia aboutone end Now break rod into 2 pieces one .4 m long and the other 1.6 mlong m1 = (.4 / 2) * 3 = .6kg         m2 =(1.6 / 2) * 3 = 2.4 kg I2 = 1/3 [ .6 * .42 + 2.4 *1.62] = 2.08 kg-m2 Percentage change = (2.08 - 4) / 4 * 100 = -48% Percentage change = (2.08 - 4) / 4 * 100 = -48%

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