Disk with a Hole Rolling in a Semicircular Well

disk radius

0.286

trace center:

mass

disk

hole

all three

hole fraction

0.67

animation

phase angle

1.09

speed

The center of mass of a disk with a hole is offset from the disk's geometric center, so that as the disk rolls in a circular well its motion is irregular.

This Demonstration simulates the motion of a disk of radius

R

with a hole of radius

r

at a distance

R-r

from the center. Lagrangian mechanics are used to get the equation of motion for the animation and to compute the traces of the center of mass and the geometric centers of the disk and the hole.