Spinning bottle on the surface of the water

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Discussion Overview

The discussion revolves around the dynamics of a cylindrical bottle spinning on the surface of water, focusing on how to calculate the time duration of its spinning motion. Participants explore theoretical and practical aspects of the problem, including stability, energy dissipation, and the effects of water viscosity.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that a spinning bottle is likely to be unstable and may not remain vertical long enough to analyze its motion effectively.
  • Another participant proposes that finite-element analysis could provide approximations, but expresses doubt about the existence of an analytic solution to the problem.
  • It is mentioned that viscous dissipation of rotational energy will eventually bring the bottle to a stop, with references to the mass, angular momentum, initial energy, viscosity of water, and surface area as relevant factors for calculations.
  • One participant notes that the water will start moving with the bottle after some time, and that angular momentum conservation will allow it to continue spinning, albeit at a diminishing rate.
  • There is a clarification regarding the orientation of the bottle, with one participant emphasizing that the bottle is horizontal, not vertical.
  • Another participant reiterates the idea that simulations may yield results, but maintains that the bottle will likely never stop completely and that an analytic solution is improbable.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the stability of the bottle, the feasibility of analytic solutions, and the nature of the bottle's motion over time. The discussion remains unresolved with no consensus reached.

Contextual Notes

Participants note limitations regarding the assumptions made about the bottle's stability and the complexity of the motion, as well as the dependence on various physical parameters that may not be fully defined.

sceptic
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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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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.
 
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.
 
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).
 
Or, rolling horizontally across the surface.
 
For a realistic bottle - probably, yes.
 
mfb said:
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.

No, it is not vertical! The axes and the bottle is horizontal!
 
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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