Re: [Phys-L] Math List Serves

[Brian Whatcott <betwys1@sbcglobal.net>]

 I see that you (or I) were hoist by a petard. A punctuation petard, no less. I will capitalize  to exaggerate the point:Consider a LONG uniform thin rigid rod of NEGLIGIBLE THICKNESS AND LENGTH,           L....
It were the comma that done it, yer honor.    On Tuesday, September 20, 2022 at 12:39:36 PM CDT, David Bowman <david_bowman@georgetowncollege.edu> wrote:  
 
 Regarding Brian W's claim/observation:

> This...Consider a long uniform thin rigid rod of negligible
> thickness and length, L precariously balanced and standing
> vertically upright at rest on a frictionless horizontal floor.
> ...is a contradiction in terms.

It's not so much a contradiction in terms as it an idealization that is not realizable for any typically usefully long period of time.  That is why in the next sentence I said, "Since this situation is unstable it soon tips over and falls down"  The realizable time scale over which it remains in an upright position very close to vertical depends on just how carefully the initial preparation is done, and how significant the complicating non-ideal complicating factors happen to be.  One complicating factor that can't be just arbitrarily swept under the rug and ignored by simply imagining a further degree of idealization is the Heisenberg Uncertainty Principle.

But perhaps you thought my use of the word "balanced" was intended to convey the implication of being indefinitely stable in an upright position.  What I meant by the word was to be simply as vertical and as at rest as it is realizable to be as an initial condition within the degree of idealization being considered.  But that mouthful of qualifying words would have made my already overly pedantic phraseology for the problem only a lot worse.

An unstable situation like this reminds me of a homework problem I remember from Schiff's Quantum Mechanics book that asked the maximum number of times an ideal perfectly elastic ping pong ball dropped directly on top of another identical--but rigidly fixed one from a height of 10 times its radius in a vacuum can bounce on top of it until it goes flying off in some direction because of the Uncertainty Principle prevents the initial conditions for the problem from being perfectly ideal.  As I recall from my student days, I think the answer was something like 8 bounces.

David Bowman
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