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 4.7 kg and diameter 0.34 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.

Express your answer using two significant figures.

Answer 1

using conservation of angular momentum

I _initial = I _final

and moment of inertia for wheel is

I_wheel = M R²/2

= 4.7 x 0.17²/2

I_wheel = 0.067915 kg-m²

now

the moment of inertia for clay is,

I_clay = M R²/2

= 2.8 x 0.08²/2

= 0.00896 kg-m²

I_wheelinitial = ( I_wheel + I_clay ) _final  

0.067915 x 1.7 = ( 0.067915 + 0.00896 ) _final  

_final = 0.067915 x 1.7 / ( 0.067915 + 0.00896 )

_final = 1.50 rev/sec

the frequency of the wheel after the clay sticks to it is _final = 1.50 rev/sec