Question

A potter's wheel is rotating around a vertical axis through its center at a frequency of 1.6 rev/s. The wheel can be considered a uniform disk of mass 5.8 kg and diameter 0.48 m. The potter then throws a 2.0-kg chunk of clay, approximately shaped as a flat disk of radius 7.6 cm, onto the center of the rotating wheel.

What is the frequency of the wheel after the clay sticks to it? Express your answer using two significant figures.

Answer 1

Moment of inertia of disk through center and perpendicular to plane = 0.5mr^2

Angular momentum is conserved
Initial angular momentum = Final angular momentum

Initial moment of inertia * Initial angular frequency = Final moment of inertia * Final angular frequency

(0.5*5.8*(0.48/2)^2) * 2 π * 1.6 = ((0.5*5.8*(0.48/2)^2) + (0.5*2*(0.076)^2)) * 2πf

f = ((0.5*5.8*(0.48/2)^2) * 1.6) / ((0.5*5.8*(0.48/2)^2) + (0.5*2*(0.076)^2))

f = 1.55 rev/s

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