Question

A particular horizontal turntable can be modeled as a uniform disk with a mass of 180 g and a radius of 30.0 cm that rotates without friction about a vertical axis passing through its center. The angular speed of the turntable is 2.00 rad/s. A ball of clay, with a mass of 40.0 g, is dropped from a height of 35.0 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.

Answer 1

Initial angular momentum,

Li = 0.5 MR^2w

Li = 0.5 x 0.18 x 0.30^2 x 2 = 0.016 kg m^2/sec

Final angular momentum,

Lf = ((0.5 x 0.18 x 0.3^2) + (0.04 x 0.15^2)) wf

Lf = 0.009 wf

Using law of conservation of angular momentum,

Li = Lf

0.016 = 0.009 wf

wf = 1.78 rad/sec

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