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Rigid solid

  1. Nov 13, 2004 #1
    I don't know how to solve this rigid solid problem

    Let there be a rod hanging of a string fixed to a certain point. Why is not possible for both the string and the rod to be in the same direction all the time. (it is common sense that it's impossible but how can I prove it?)

    I've tried to figure it out thinking that it is possible and look for a contradiction.

    Thanks a lot!
     
  2. jcsd
  3. Nov 13, 2004 #2
    Can you make your question clearer?
     
  4. Nov 14, 2004 #3
    I'm sorry for not explaining myself clearer. the string is attached to the rod at the center of one of its ends, no external forces are acting on it other then gravity. The thing is that the rod will start oscillating and I want to prove that it is impossible that both the rod and the string stay in the same direction (as if it were a single rod).

    What properties of the rigid solid should I use to prove it is impossible?

    Thanks again
     
  5. Nov 14, 2004 #4
    Well, it all depends on how you start it oscillating, of course (what is the initial position of the rod and string and so forth). But one thing that might be more intuitive to think about is this - how about if you had the rigid rod _above_ the string, what would the end of the string do as the rod swung to and fro?

    A further hint: the tangential acceleration at every point along a pendulum system is the same (ma=mgsinx, so the ms cancel out). Rigid bodies swing all in one line because of internal attractive forces among their constituent atoms that "drag" each other along each other - what if the forces were weaker? If every point in the string-rod system was accelerating the same, would the system remain a straight line?

    Actually, in what you're proposing, the observable effect would be miniscule because tension would work to keep the system fairly straight (assuming the rod was significantly heavier than the string). You _would_ observe a "kink" if you looked hard enough, though.

    Btw, it'd probably be useful to think some more about why ideal rigid bodies fall as a straight line in pendulum motion - that is, why the center of mass concept works. (edit: ahh, which is not to imply it doesn't work for non-rigid bodies; what i meant to say is: why the center of mass concept is so useful for examining a physical pendulum)
     
    Last edited: Nov 14, 2004
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