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??

 

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.

 

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.

 

Torque-free precession?

 

Because of there being more weight on the upper half to the one side

A brick is symmetrical about each axis.

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,

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?

 

Great. Now I've got to find a brick.

 

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

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.

 

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.

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.

 

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

 

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.

 

Got it. Sloppy reading on my part.

John

 

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.

 

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)

 

I anxiously await the further explanation. John

Sorry it's so scruffy.

 

Great. Now I've got to find a brick.

Tomorrows news:

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