B Sympathetic motion generated by cleaning Rubik's cube

[xtempore]

TL;DR Summary

An electric toothbrush placed on one of the centre pieces causes the other centre pieces to start rotating. What is happening here?

A student of mine showed me something weird the other day. He had disassembled his Rubik's cube to clean it. He removed all the corners and edges and the caps over the six centre pieces. He was using an old electric toothbrush to clean it and noticed something odd happening. When he placed the toothbrush on one of the centre pieces, some of the other centre pieces would start rotating. If he left the toothbrush on there, they would slowly pick up speed.

It was common for more than one centre piece to be rotating, but usually in different directions - I never observed any cases where all the pieces that were rotating were going the same way.

I think I have an idea of what is happening, but I'm a Maths teacher, not a Physics teacher, so happy to be corrected! I also think I only understand part of the effect.

I think that the vibration from the toothbrush is travelling through the core and because the pivots are low friction, the vibrations can randomly start the piece rotating. Once it gets going, I think that resonance then allows it to build speed.

I'm less sure about why they rotate in opposite directions. Could it be some sort of conservation of rotational momentum? I can't really see how, but I can't think why they go different ways (it's possible it can happen, but just wasn't observed).

I would love to be able to give him a more complete answer!

Thanks.

 

[sbrothy]

(BUMP)

Although I, personally, can't help, I'd like an explanation for this too. It's sounds like one of those problems MIT students train their paper writing skills on (as the egg strength paper some time ago).

Still, the absurd picture in my mind begs an explanation.

 

[Baluncore]

A loose fitting part is mounted on a pin, then a vibration is induced in the mounting pin that has a two-dimensional or circular character, so a rotation can be induced in the loose fitting part.
https://en.wikipedia.org/wiki/Gee-haw_whammy_diddle

 

[sbrothy]

A loose fitting part is mounted on a pin, then a vibration is induced in the mounting pin that has a two-dimensional or circular character, so a rotation can be induced in the loose fitting part.
https://en.wikipedia.org/wiki/Gee-haw_whammy_diddle

I just love how that name lines up with my mental picture!

Thank you.

 

[DaveC426913]

TIL the term gee haw whammy diddle, and my life is just slightly better for it.

 

[Baluncore]

I can't be sure that this explains the OP observation, because there are several ways of assembling the cube, and I don't know the motion of the brush.

 

[sbrothy]

I'm not sure anyone wants the silliness destroyed by a serious explanation. I like it as it is.

 

[xtempore]

A loose fitting part is mounted on a pin, then a vibration is induced in the mounting pin that has a two-dimensional or circular character, so a rotation can be induced in the loose fitting part.
https://en.wikipedia.org/wiki/Gee-haw_whammy_diddle

I think this might be it! Either way, I'll get myself some dowel and start putting together some geehaw whammy-diddles. First one will be going to the kid with the Rubik's cube.

It looks a lot like the same phenomenon with some equivalents and some apparent differences.
An electric toothbrush has a pivoting head that rapidly moves back and forth, so this seems like it would produce a similar type of regular vibration to the rubbing stick moving across the regularly spaced notches (actually, the toothbrush will be more consistent).
The GHWD requires a hole that is much larger than the nail. I think the axle is a reasonably close fit, but perhaps being low-friction is the important part here.
But I think he says the GHWD works because of asymmetry, whereas I think the Rubik's cube parts would be highly symmetrical.

Overall, it does feel like a very good explanation though. I'm curious if you made a GHWD with more than one propeller, what might happen? Even just doing one with a propeller on each end could be interesting. I *think* that one propeller would move CW and the other CCW - although if you are looking from a fixed point, they would appear to be moving in the same direction.

Who knows, maybe this means that entangled particles are just the gee-haw whammy diddles of the quantum world.

 

[Baluncore]

The GHWD requires a hole that is much larger than the nail. I think the axle is a reasonably close fit, but perhaps being low-friction is the important part here.

It is a compromise. Notice how a shaft, only slightly smaller than the hole, can counter-rotate within the hole, by rolling around the wall. That requires high friction between the shaft and the hole, in effect an epicyclic gear wheel, where the teeth on the gears are the surface asperities.

But I think he says the GHWD works because of asymmetry, whereas I think the Rubik's cube parts would be highly symmetrical.

If the propeller is asymmetric, then it can be driven by the pin, even through zero friction. The vibration is asymmetric, either left or right polarised depending on which side has the vibration phase delayed, through finger contact. It appears that asymmetry of different parameters, is required under different modes of operation.

I *think* that one propeller would move CW and the other CCW - although if you are looking from a fixed point, they would appear to be moving in the same direction.

This is a shaft unbalance situation. If one propeller point on the shaft is vibrating in an ellipse of one amplitude and phase, while another propeller point has a different amplitude and phase, but at the same frequency, then there will be a node somewhere along the line of the shaft that has zero movement. That node can be between the two points, or beyond the system. If the node is between the two points, then the propellers will counter-rotate, if the node is beyond the propellers, then they will rotate in the same direction. The position of the node is determined by the shaft's degree of freedom and mode of vibration, effectively, the way you hold the shaft.

P.S.
"Gee" and "haw" are traditional voice commands used to direct draft animals, like horses and mules, to turn. "Gee" means to turn right, and "haw" means to turn left. "Hup" or "Giddy-up" means go faster or switch gait up, "whoa" means stop.

 

[sbrothy]

The explanation for "whoa" actually explains a lot.

 

[Lnewqban]