I was considering the toy Euler's Disk, a video can be found here: http://www.youtube.com/watch?v=mVl2CBG_h2s

I was interested in understanding the behavior of the disk particularly in vacuum and in a superfluid.

I Know that Euler's disk in vacuum runs slightly longer than usual and that most of the dissipation of energy is due to rolling friction. Suppose it was suspended in a superfluid. since they have (If I understand correctly) 0 viscosity, is running Euler's disk in a superfluid the same thing as running it in a vacuum?

Furthermore, what would be an example of an extremely smooth surface? IE is there a limit to how smooth you can make surfaces?

  • $\begingroup$ To clarify what "same thing" means, I should add, if one were to play with Euler's disk submerged in a superfluid, would it run the same amount of time as if it were to be spun in a vacuum? $\endgroup$ – frogeyedpeas Dec 21 '14 at 7:24

When considering motion in a fluid, or of a fluid, there are two types of forces to consider. Everyone immediately thinks of viscous forces, which arise from the viscosity of the fluid, and as you say these disappear in a superfluid. However there are also inertial forces that arise because the fluid has a mass. Accelerating the fluid requires a force just as accelerating any mass does. Spinning the Euler's disk in the fluid is going to require accelerating the fluid to move it around as the disk spins, and this will exert a force on the disk. So spinning the disk in superfluid helium is not the same as spinning it in a vacuum.

Having said this, in the absence of viscosity the kinetic energy isn't dissipated. I'm not sure what would happen if you did the experiment. Presumably the disk would transfer some of it's energy to making the fluid flow, but this would only be a small part of the energy. I'd also guess that as the disk slows the fluid will transfer some energy back to the disk. What the end result would be I'm not sure.

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  • $\begingroup$ My gut was making me wonder about the moving mass, but you bring a curious point, I have no idea how the fluid will affect back the disk $\endgroup$ – frogeyedpeas Dec 21 '14 at 8:59

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