Discover the Fascinating Physics of the Tippe Top | Princeton Physics Dept.

[Bob S]

Here is an article via the Princeton Physics Dept. on the Tippe Top (Tipsey Turvy Top) that will flip upside down when you spin it. The flipping is apparently due to contact torque.

http://www.google.com/url?sa=t&source=web&cd=2&sqi=2&ved=0CBkQFjAB&url=http%3A%2F%2Fwww.physics.princeton.edu%2F~mcdonald%2Fexamples%2Fmechanics%2Fpliskin_ajp_22_28_54.pdf&ei=7ge9TL3mG8bMswarkqTJDQ&usg=AFQjCNEyFqkkE6PtYF8gf_5fD-MhV0xwzQ&sig2=IYVOWaouG1Wrej123gMX0w

This is unrelated to the "polhode rolling on the herpolhode in the invariable plane" instability discussed in Goldstein "Classical Mechanics", which can be easily demonstrated with a book (held shut with a rubber band).

Bob S

 

[FREEDOM2]

Here is an article via the Princeton Physics Dept. on the Tippe Top (Tipsey Turvy Top) that will flip upside down when you spin it. The flipping is apparently due to contact torque.

http://www.google.com/url?sa=t&source=web&cd=2&sqi=2&ved=0CBkQFjAB&url=http%3A%2F%2Fwww.physics.princeton.edu%2F~mcdonald%2Fexamples%2Fmechanics%2Fpliskin_ajp_22_28_54.pdf&ei=7ge9TL3mG8bMswarkqTJDQ&usg=AFQjCNEyFqkkE6PtYF8gf_5fD-MhV0xwzQ&sig2=IYVOWaouG1Wrej123gMX0w

This is unrelated to the "polhode rolling on the herpolhode in the invariable plane" instability discussed in Goldstein "Classical Mechanics", which can be easily demonstrated with a book (held shut with a rubber band).

Bob S

So if the M&M was spinning on a perfectly frictionless surface in a vacuum would it just spin like a sphere does with friction?

 

[Archosaur]

So if the M&M was spinning on a perfectly frictionless surface in a vacuum would it just spin like a sphere does with friction?

I don't know if I follow, but you're right in that there would be no reason for it to right itself.

 

[Bob S]

So if the M&M was spinning on a perfectly frictionless surface in a vacuum would it just spin like a sphere does with friction?

Actually not. For a sphere, the point of contact, and the point of vertical force mg, is always directly below the center of gravity (CG). For an M&M, the force is directly below the CG only for two special orientations. When this force is not directly below the CG, there is a torque on the M&M, even if the contact is frictionless.

Bob S

 

[D H]

Here is an article via the Princeton Physics Dept. on the Tippe Top (Tipsey Turvy Top) that will flip upside down when you spin it. The flipping is apparently due to contact torque.

http://www.google.com/url?sa=t&source=web&cd=2&sqi=2&ved=0CBkQFjAB&url=http%3A%2F%2Fwww.physics.princeton.edu%2F~mcdonald%2Fexamples%2Fmechanics%2Fpliskin_ajp_22_28_54.pdf&ei=7ge9TL3mG8bMswarkqTJDQ&usg=AFQjCNEyFqkkE6PtYF8gf_5fD-MhV0xwzQ&sig2=IYVOWaouG1Wrej123gMX0w

Here is a much more recent (and much longer) paper that also attributes the flipping to frictional losses. Moreover, they show that without frictional losses the inversion cannot occur.

Bou-Rabee et al. (2008), Dissipation-Induced Heteroclinic Orbits in Tippe Tops, SIAM Review, 50:2, 325-344
http://authors.library.caltech.edu/10958/1/BOUsiamr08.pdf

 

[Bob S]

See video of Tippe Top at

http://www.google.com/url?sa=t&sour...0rlUW8aGl1G1xVcww&sig2=_XCXwQQywzoCS56Rbz7IzA

Maybe angular momentum plus friction force converts kinetic energy into lifting the center of gravity.

Bob S

 

[FREEDOM2]

Actually not. For a sphere, the point of contact, and the point of vertical force mg, is always directly below the center of gravity (CG). For an M&M, the force is directly below the CG only for two special orientations. When this force is not directly below the CG, there is a torque on the M&M, even if the contact is frictionless.

Bob S

Thanks for explaining! I thought that origination of the torque was due to the friction...