Re: Axis of rotation

On Tue, 31 Oct 2006, matt271829-news@xxxxxxxxxxx wrote:

matt271829-news@xxxxxxxxxxx wrote:
Andy Resnick wrote:
It gets a little more complicated than that- some axes are more stable
than others. Tossing a book in the air will demonstrate this. The book
has three axes of rotation, lines that pass through the center of the
book perpendicular to the endfaces. Two of those axes are stable, one
is unstable, and trying to rotate the book through the unstable axis
will cause wobble while the other two axes allow stable rotation.

Thanks Andy... Assuming that the book is a rigid cuboid, I don't really
see why one of the three axes passing through its centre perpendicular
to a pair of faces should be unstable while the other two are stable. I
would have thought all three would be equivalent in this respect, since
there's no essentially different characteristic that can distinguish
one from any other?

Sorry... to perhaps answer my own question, comparing your post with
Mike Fontenot's reply, I think I might be misunderstanding the meaning
of "stable" here. All three axes are "stable" in the sense that
*theoretically* the book will continue rotating along that axis
forever, but only two are "stable" in the sense that they are robust
against the tiny perturbations that will inevitably occur in practice?

Essentially, this is what "stable" means in physics - stability vs small perturbations. Also, the 3 different axes of a bookoid are different. One has the largest moment of inertia, one has the smallest, and one has one that is intermediate. One might expect at least one of the two first cases to be stable, but the 3rd is unlikely to be so.

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html

.

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