If you take a hardboiled egg and put it on a table and start to spin it, if you

Question

If you take a hardboiled egg and put it on a table and start to spin it, if you spin it fast enough it will start to spin in an upright position. What is the angular velocity needed for this transition to occur?

Is energy conserved in the transition? Must there be some imperfection in the egg for the transition to occur?

Assume a prolate spheroid egg of constant density. If that doesnt work, assume its center of mass is shifted abit, if that dont work, assume an egg.

Edit: One is allowed to use simpler shapes of the same symmetry type, to avoid messy integrals.

And most importantly, can you explain without equations, why does the egg prefer to spin in an upright position ?

Explanation / Answer

In my oppinion this problem is equivalent to the Tippe_top, with the difference of the egg not turning around 180 degrees but 90 degrees. The underlying physics should be the same, since the center of mass and the geomtric center are not being the same. The egg should be a little bit easier to calculate, since its geometric shape is not that horrible. (However its still way over my head). As you already pointed out, this behaviour is not possible on a frictionless table. For some readings see:

http://en.wikipedia.org/wiki/Tippe_top

http://arxiv.org/PS_cache/chao-dyn/pdf/9501/9501008v1.pdf

http://www.jstor.org/pss/2102374

The last two links are quite an extensive discussion about the involved physics. A more basic introduction to this topic is

http://www.physik.uni-augsburg.de/~wobsta/tippetop/literature.shtml.de

Unfortunatelly, this website is only available in German. However you might take the above links as as starting point for furhter readings.

Greetings

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