Disk with a Hole Rolling in a Semicircular Well
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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.
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Contributed by: Erik Mahieu (April 2014)
Open content licensed under CC BY-NC-SA
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Consider a disk of mass and radius
. The disk has a hole with radius
at a distance
from its center. The mass cut out by the hole is
.
The potential energy of the disk plus hole is .
The kinetic energy of the system is ,
where
is the moment of inertia of the disk plus hole.
The Lagrangian gives the equation of motion:
.
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