| Conservation of
When Euler's Disk is spun, the disk contains both potential and kinetic energy. The potential
energy is given to the disk when it is placed upright on its side. The kinetic energy is given to the disk when it is spun
on the mirrored base. Euler's Disk would spoll (i.e., spin and roll) forever it it were not for friction and
Another way of
describing how Euler's Disk operates is by considering the disk's angular momentum. Like a top, Euler's Disk uses its
angular momentum to hold itself upright. As the disk spolls around in a circle it is held in place by a balance of the
gravitational force pulling the disk down and the force applied by the mirror base which holds the disk up. Again, if it
were not for friction and vibration, the disk would rotate for a very long time.
Using Euler's equations of motion - and several assumptions - one can
show that as the disk loses energy, the soaring pitch produced by the rolling point of contact increases towards infinity,
as the inverse square root of the angle alpha. This result, is a beautiful example of the rather subtle and elegant motion
of the toy. The curious student will be amazed at the number of interesting problems one can solve concerning the motion
of this little toy. Papers on the motion of Euler's Disk are available from the inventor as well as a non-vector, harmonic solution in .pdf
**There has been discussion about an interesting geometry/optics question (for the past 20 years) concerning the the figure-eight pattern that appears on the side of Euler's Disk during motion - when illuminated with a light source. To date, the most interesting input concerns a curve from differential geometry called "Viviani's curve."
Any published technical paper on the figure eight will earn yet another custom and signed Euler's disk - just email the inventor.
Some physics for teachers:
Excel worksheet with experiments:
Excel worksheet (new)
The Sounds of Euler's Disk:
LISTEN to the sound Euler's Disk makes as it spolls to infinity! Note: audio file is in WAV format.
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