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Spinning bottle on the surface of the water

  1. Jan 11, 2015 #1
    Let us suppose that a cylindrical bottle is on the surface of the water (filled with air for simplicity). A little spin is given to the bottle makes it rotating around the symmetry axis of the cylinder. After a while the bottle stops rotating. How to calculate the time duration of spinning?
     
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  3. Jan 11, 2015 #2

    mfb

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    Anything that looks like a bottle is probably to unstable to keep vertical long enough.
    I'm sure a finite-element analysis can give some approximation, and I'm also quite sure that there is no analytic solution to the problem. In a purely theoretical situation, the bottle will get slower and slower without fully stopping.
     
  4. Jan 11, 2015 #3

    Bystander

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    Viscous dissipation of the rotational energy will bring it to a full stop. You know the mass of the bottle, it's angular moment of inertia, the initial energy, the viscosity of water, and the surface area of the bottle in contact with the water. From there it's the usual bookkeeping problem.
     
  5. Jan 12, 2015 #4

    mfb

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    The water will start moving together with the bottle (but won't do that initially) - and in the absence of external torque, angular momentum conservation will always keep it spinning a bit (at some point it becomes negligible).
     
  6. Jan 12, 2015 #5

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    Or, rolling horizontally across the surface.
     
  7. Jan 12, 2015 #6

    mfb

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    For a realistic bottle - probably, yes.
     
  8. Jan 23, 2015 #7
    No, it is not vertical! The axes and the bottle is horizontal!
     
  9. Jan 23, 2015 #8

    mfb

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    Ah, okay.
    Still, simulations will give some result, it will probably never stop completely, and I am quite sure there is no analytic solution.
     
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