A particular horizontal turntable can be modeled as a uniform disk with a mass o

Question

A particular horizontal turntable can be modeled as a uniform disk with a mass of 190 g and a radius of 22.0 cm that rotates without friction about a vertical axis passing through its center. The angular speed of the turntable is 4.00 rad/s. A ball of clay, with a mass of 50.0 g, is dropped from a height of 25.0 cm above the turntable. It hits the turntable at a distance of 15.0 cm from the middle, and sticks where it hits. Assuming the turntable is firmly supported by its axle so it remains horizontal at all times, find the final angular speed of the turntable-clay system. rad/s

Explanation / Answer

here

Itable * wi = 0.5 * M * R^2 * wi = 0.5 * 0.19 * 0.22^2 * 4 = 0.018392 kg m^2 /s

then

0.018392 = Itotal * wf = (Itable + Iball ) * wf = ( 0.5 * M * R^2 + m * r^2) * wf

wf = 0.018392 / ( 0.5 * 0.19 * 0.22^2 + 0.05 * 0.15^2)

wf = 3.21 rad/s

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