Spinning bottle on the surface of the water

[sceptic]

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?

 

[mfb]

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.

 

[Bystander]

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.

 

[mfb]

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).

 

[Bystander]

Or, rolling horizontally across the surface.

 

[mfb]

For a realistic bottle - probably, yes.

 

[sceptic]

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!

 

[mfb]

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