During the last week of class, a professor performs a classroom demonstration us

Question

During the last week of class, a professor performs a classroom demonstration using a large wooden turntable in the shape of a flat uniform disk. The turntable has radius R = 1.00 m and a total mass of M = 4.00 kg. The turntable is initially rotating at angular velocity ?i = 10.00 rad/s about a vertical axis through its center. Suddenly, the professor vertically drops a non-spinning uniform plank on the spinning turntable. You may model the plank as a uniform rod with length L equal to the diameter of the turntable. The plank mass is m = 2.00 kg. The plank lands on the turntable along the turntable

Explanation / Answer

Idisk = .5mdiskR^2 Iblock = mblockR^2 L = Idisk?i = .5mdiskR^2?i = (Idisk + 2Iblock)? = (.5mdiskR^2 + 2mblockR^2)?f ?f = .5mdiskR^2?i/(.5mdiskR^2 + 2mblockR^2) = mdisk?i/(mdisk + 4mblock) = 2*100/(2 + 4*.5) = 50

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