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Spinning top question

by Cexy
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Cexy
#1
Dec2-05, 04:47 AM
P: 70
Do you get sweets called Skittles in America, or the rest of the world?



We get them in the UK - they're fruit-flavoured sweets in the various colours of the rainbow. The other day, whilst savouring a pack in the cafe at the maths dept, I noticed a particularly strange property of Skittles.

Your average skittle is shaped like you chopped a section off the side of a sphere, then got two of them and stuck them together. It's kind of hard to explain, and I don't know the mathematical name for such a shape, but hopefully this picture will give you the idea:



So anyway. Take a handy Skittle, put it on the table, and then spin it as fast as possible. You'll notice that it starts to wobble a bit, and then all of a sudden it flips up onto its side, so that it's spinning on its edge rather than its bottom! I imagine that this is is just because that's a more stable mode of rotation at higher speeds, but I've been unable to derive that mathematically. So if anyone could help me out, I'd be more than grateful! I'm happy as Larry with Lagrangian dynamics, so feel free to use whatever tools you have at your disposal - I just want an answer!

Ta :)
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dicerandom
#2
Dec3-05, 12:56 AM
P: 308
I think that the mode where it's spinning like a flying saucer should be the stable one, that's the major axis of symmetry. It should fall back down to that rotation towards the end of its movement. I would expect that if the Skittle is hopping up onto its edge and rotating about one of the minor axes of symmetry it's due to roughness of the surface or some instability in the rotation imparted during the initial spin.
Cexy
#3
Dec3-05, 09:03 AM
P: 70
Quote Quote by dicerandom
I think that the mode where it's spinning like a flying saucer should be the stable one, that's the major axis of symmetry. It should fall back down to that rotation towards the end of its movement.
Yeah, it does. It starts in 'flying saucer' mode, then jumps up to its edge, and then winds back down to end up lying on its belly.
I would expect that if the Skittle is hopping up onto its edge and rotating about one of the minor axes of symmetry it's due to roughness of the surface or some instability in the rotation imparted during the initial spin.
What do you mean by the 'major' axis of symmetry? The one with greatest moment of inertia?

dicerandom
#4
Dec3-05, 01:18 PM
P: 308
Spinning top question

Quote Quote by Cexy
What do you mean by the 'major' axis of symmetry? The one with greatest moment of inertia?
Right.

... evidently I need 10 characters ...

Edit:

I've thought about it some more, and while it's true that in this case the major axis of symmetry has the largest moment of inertia that is not true in general. I knew there was something fishy about what I'd written. The major axis of symmetry is, well, the one which is the most symmetric ;) For a cylinder, for instance, the major axis of symmetry is the one which goes straight down the middle of it. In that case it has the smallest moment of inertia.
Danger
#5
Dec3-05, 01:27 PM
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Smarties and M & M's are the same shape. I wonder if they do it too, or if it's strictly a fruit phenomena.
Cexy
#6
Dec4-05, 08:01 AM
P: 70
Quote Quote by Danger
Smarties and M & M's are the same shape. I wonder if they do it too, or if it's strictly a fruit phenomena.
This topic certainly deserves more investigation. Research grant, anyone?


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