# Spinning bottle on the surface of the water

• sceptic
In summary, the conversation discusses the spinning of a cylindrical bottle on the surface of water and the difficulty of calculating the duration of the spin. It is suggested that a finite-element analysis can provide an approximation, but there is no analytic solution to the problem. The possibility of the bottle never fully stopping is also mentioned. The conversation ends with a clarification that the bottle is horizontal, not vertical.

#### 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?

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.

## 1. How does a bottle spin on the surface of the water?

A bottle can spin on the surface of the water due to the principle of angular momentum. When the bottle is set in motion by a person's hand, the water molecules around it also start to move and create a circular motion. This motion creates a force that keeps the bottle spinning.

## 2. Why does the bottle rotate in a circular motion instead of moving in a straight line?

The circular motion of the bottle is due to the surface tension of the water. This surface tension creates a force that acts perpendicular to the surface of the water, causing the bottle to rotate in a circular motion instead of moving in a straight line.

## 3. What factors affect the speed at which the bottle spins on the water?

The speed at which the bottle spins on the water is affected by several factors, including the initial force applied to the bottle, the surface tension of the water, and the shape and weight distribution of the bottle. A larger force, lower surface tension, and a more balanced bottle will result in a faster spin.

## 4. Can the bottle spin indefinitely on the surface of the water?

No, the bottle cannot spin indefinitely on the surface of the water. Eventually, the energy from the initial force applied to the bottle will dissipate, causing the bottle to slow down and eventually stop spinning. The surface tension of the water also plays a role in how long the bottle can spin, as it can break at a certain point, causing the bottle to stop spinning.

## 5. How can I make the bottle spin faster on the surface of the water?

To make the bottle spin faster on the surface of the water, you can increase the initial force applied to the bottle, decrease the surface tension of the water by adding a surfactant, or use a more streamlined and evenly weighted bottle. However, be careful not to apply too much force or decrease the surface tension too much, as this can cause the bottle to spin out of control or sink into the water.