Rolling Cylinder with a Hole

radius

2

density

10

initial angular velocity

1

time to watch animation

10

release system

A cylinder of radius

r

has a cylindrical hole of radius

r/2

as shown in the figure. Vary the radius, density, and initial angular velocity to see the cylinder move in some interesting ways.

Since this is a one degree of freedom system, only one equation of motion is needed to fully locate it. This equation is:

0=2ϱπ

4

r

θ'θ''3764-18cos(θ)+18ϱπ

4

r

3

θ'

sin(θ)+18ϱπg

3

r

θsin(θ)

.