Euler's Disk
Euler's Disk, invented between 1987 and 1990 by Joseph Bendik,[1] is a trademarked scientific educational toy.
[2] It is used to illustrate and study the dynamic system of a spinning and rolling disk on a flat or curved surface.
[4] Joseph Bendik first noted the interesting motion of the spinning disk while working at Hughes Aircraft (Carlsbad Research Center) after spinning a heavy polishing chuck on his desk at lunch one day.
As the disk releases the initial energy given by the user and approaches a halt, its rotation about the vertical axis slows, while its contact point oscillation increases.
Lit from above, its contact point and nearby lower edge in shadow, the disk appears to levitate before halting.
The commercial toy consists of a heavy, thick chrome-plated steel disk and a rigid, slightly concave, mirrored base.
Included holographic magnetic stickers can be attached to the disk, to enhance the visual effect of wobbling.
Commercial disks provide a more effective demonstration of the phenomenon, having an optimized aspect ratio and a precision polished, slightly rounded edge to maximize the spinning/rolling time.
A spinning/rolling disk ultimately comes to rest quite abruptly, the final stage of motion being accompanied by a whirring sound of rapidly increasing frequency.
In fact, the precession rate of the axis of symmetry approaches a finite-time singularity modeled by a power law with exponent approximately −1/3 (depending on specific conditions).
In the limit of small angle (i.e. immediately before the disk stops spinning), air drag (specifically, viscous dissipation) is the dominant factor, but prior to this end stage, rolling friction is the dominant effect.
Since the center of the disk and the point of contact are instantaneously at rest (assuming there is no slipping) axis
The levitation illusion can be enhanced by optimizing the curve of the lower edge so the shadow line remains high as the disk settles.
Disk imperfections, seen in shadow, that could hamper the illusion, can be hidden in a skin pattern that blurs under motion.
In the early 2000s, research was sparked by an article in the April 20, 2000 edition of Nature,[4] where Keith Moffatt showed that viscous dissipation in the thin layer of air between the disk and the table would be sufficient to account for the observed abruptness of the settling process.
His first theoretical hypothesis was contradicted by subsequent research, which showed that rolling friction is actually the dominant factor.
is given by Moffatt's theoretical work inspired several other scientists to experimentally investigate the dissipative mechanism of a spinning/rolling disk, with results that partially contradicted his explanation.
These experiments used spinning objects and surfaces of various geometries (disks and rings), with varying coefficients of friction, both in air and in a vacuum, and used instrumentation such as high speed photography to quantify the phenomenon.
In the 30 November 2000 issue of Nature, physicists Van den Engh, Nelson and Roach discuss experiments in which disks were spun in a vacuum.
[8] Van den Engh used a rijksdaalder, a Dutch coin, whose magnetic properties allowed it to be spun at a precisely determined rate.
They pointed out that Moffatt's theoretical analysis would predict a very long spin time for a disk in a vacuum, which was not observed.
[9] Later work at the University of Guelph by Petrie, Hunt and Gray[10] showed that carrying out the experiments in a vacuum (pressure 0.1 pascal) did not significantly affect the energy dissipation rate.
Petrie et al. also showed that the rates were largely unaffected by replacing the disk with a ring shape, and that the no-slip condition was satisfied for angles greater than 10°.
Another work by Caps, Dorbolo, Ponte, Croisier, and Vandewalle[11] has concluded that the air is a minor source of energy dissipation.
The major energy dissipation process is the rolling and slipping of the disk on the supporting surface.
It was experimentally shown that the inclination angle, the precession rate, and the angular velocity follow the power law behavior.
Spinning the ring in a vacuum had no identifiable effect, while a Teflon spinning support surface gave a record time of 51 seconds, corroborating the claim that rolling friction is the primary mechanism for kinetic energy dissipation.
[citation needed] Various kinds of rolling friction as primary mechanism for energy dissipation have been studied by Leine[12] who confirmed experimentally that the frictional resistance of the movement of the contact point over the rim of the disk is most likely the primary dissipation mechanism on a time-scale of seconds.
Euler's Disks appear in the 2006 film Snow Cake and in the TV show The Big Bang Theory, season 10, episode 16, which aired February 16, 2017.
[13] The principles of the Euler Disk were used with specially made rings on a table as a futuristic recording medium in the 1960 movie The Time Machine.
