# Spinning box trick question

Discussion in 'Physics' started by studiot, Jan 25, 2010.

1. ### studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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Take a brick shaped object such as an empty matchbox or a box of tissues.

Spin the box freely in the air about each of its three axes, x,y and z.

You can do this by holding opposite faces at the corners and imparting a twisting motion as you throw it up.

You will find that the box spins sedately about two of the three axes. However it wobbles and oscillates as it turns about the third.

Explanations??

2. ### davebee Well-Known Member

Oct 22, 2008
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Well I can add the observation that solid bodies have three principle axes of rotation, and rotations about the axis of greatest or of least angular momentum are stable but rotations about other axis is not stable, but I can't really say "why" this is the case.

3. ### retched AAC Fanatic!

Dec 5, 2009
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the centrifugal force tries to "center" the mass. Because of there being more weight on the upper half to the one side, the lower half to the other, the force tries to center them.

4. ### BillO Distinguished Member

Nov 24, 2008
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Torque-free precession?

5. ### studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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A brick is symmetrical about each axis.

A disk will happily spin about all three axes. A brick will not.

Did anyone try this and find out along which axis the instability lies?

6. ### retched AAC Fanatic!

Dec 5, 2009
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Great. Now I've got to find a brick.

7. ### jpanhalt AAC Fanatic!

Jan 18, 2008
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Yes, but why? If the moments of inertia (A,B, and C) about axes a,b and c, respectively, are A<B<C, then the unstable axis is b.

Unfortunately all of the hits I got on the Internet to explain it were paid subscriptions or too complicated for me.

John

edit: Just noted davebee said the same thing. Sorry.
edit#2: Wolfram gives equations for stability about the two stable axes, but not the third, and doesn't derive them. It refers to precessional constant, which is where I got lazy.

Last edited: Jan 26, 2010
8. ### studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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John is correct as usual. It's a Chaos thing brought about by instability in the governing second order differential equation which is similar to the series LCR one I posted recently in another thread.

Retched, make sure it is a lead brick and your toe is strategically placed beneath.

I will explain further when you guys are done.

9. ### jpanhalt AAC Fanatic!

Jan 18, 2008
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Actually, davebee was the first to give the correct result here. Although, I remembered this problem being presented in my undergraduate physics class (circa 1963).

I anxiously await the further explanation. John

10. ### studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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I have already observed why davebee's post was inaccurate.

The original mechanics was derived in 1760 by Euler, so no one has a patent on it.

Last edited: Jan 26, 2010
11. ### jpanhalt AAC Fanatic!

Jan 18, 2008
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Got it. Sloppy reading on my part.

John

12. ### BillO Distinguished Member

Nov 24, 2008
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Torque-free precession is indeed a solution to Euler's equations, and one of the only ones that existed when I studied this back when. I remember reading about a couple of guys that did some more recent (circa mid 90's) work on this, though I never read the dissertation.

13. ### retched AAC Fanatic!

Dec 5, 2009
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Ok, so i spun the brick over and over. Even created a little jig to spin it whilst I observed.. All I got out of it was a broken toe. (thanks studiot)

14. ### studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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Sorry it's so scruffy.

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15. ### spinnaker AAC Fanatic!

Oct 29, 2009
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Tomorrows news:

Baltimore man dies of concussion from brick he threw into the air.