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 240 g and a radius of 28.0 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 30.0 g, is dropped from a height of 30.0 cm above the turntable. It hits the turntable at a distance of 15.0 cmfrom 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.

Explanation / Answer

from conservation of angular momentum

I1 w1 = I2 w2

I1 = mr^2 /2 = 0.240*(0.28)^2 /2 = 0.009408 kg-m^2

angular speed w1 = 4 rad/s

I2 = mr^2/2 + MR^2 = 0.009408 + 0.030(0.15)^2 = 0.010083 kg-m^2

0.009408*4 = 0.010083 w2

w2 = 3.732 rad/s

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