Question

A potter's wheel is rotating around a vertical axis through its center at a frequency of 1.7 rev/s. The wheel can be considered a uniform disk of mass 5.0 kg and a diameter of 0.32 m. The potter then throws a 2.8-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel.

What is the frequency of the wheel after the clay sticks to it? Ignore friction.

Answer 1

Given the mass of the potters wheel is M = 5kg and its radius is R = 0.32m. The initial frequency of the system is f(i)= 1.7m/s. The wheel can be considered as a uniform disc. So, the moment of inertia of the wheel is,

The mass of the chunk of clay is m = 2.8kg and the radius of the clay is r = 8cm. The chunk of clay can also be considered as a flat disk. So the moent of inertia of the chunk of clay is,

Let I(i) and I (f) be the initial and final moment of inertia of the system, (i) and (f) be the initial and final angular velocity of the system and f(f) be the final frequency of the system. Now applying law of conservation of angular moomentum,

So the frequency of the wheel after the clay sticks to it is 1.64 rev/s.