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We also asked some scientists for their explanations. What a great discussion we had! Even they did not agree on a single explanation. Each had a different perspective. Take a look. Do you get any ideas from what the scientists are saying?
I believe the explanation could simply be related to the amount of rotational inertia you are communicating to your bottle/water system.
- Empty bottle, bottle half-filled with water frozen to ice, bottle completely full of water: The object is more or less behaving as a solid body.
- Bottle half-filled with liquid water: Part of the water is not rotating when you flip the bottle, because it has a free boundary, that is, a surface not in contact with the bottle.
In other words, you should be intuitively adapting the initial torque according to the weight of the object.
Thanks. Great comment! The three flipping actions for the bottle acting as a solid body are very similar. But what about a reaction to the weight? This is why we included in the activity the half-filled bottle with water frozen to ice. There is little difference between the weight of a bottle half-filled with liquid water and a bottle half-filled with ice. So as far as a physiological reaction goes, both bottles would feel essentially the same and would behave the same until the moment of release. At that point the liquid water no longer has to take the shape of its container. As you mention, the free boundary of the liquid is important.
I believe this goes back to Newton's first law, which states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. Putting it in another way, momentum is conserved.
In an “empty bottle,” the bottle is filled with air; however, the total mass of the air is significantly less than that of the bottle. Thus, once we imparted rotation to the bottle, the momentum of the bottle was sufficient to carry the air within it around as it rotated. In other words, if you would have tossed the bottle high up, it would have made multiple turns before falling back into your hand.
In a “water-filled” bottle, the water was behaving much like a solid body. There is probably some internal movement, but it is limited. As a solid body, the bottle will continue to flip much like a truly empty bottle. The internal flow of the fluid inside will eventually consume sufficient rotational energy and the bottle will quit flipping.
In a half-filled bottle, the water is free to flow from one end of the bottle to the other end. When we flip the bottle, we “poured” the water from one end to the other. Unless we continue flipping the bottle, there is insufficient force to move the water from that end of the bottle back to the initial end. However, if the mass of the bottle is sufficiently high relative to that of the water within, then perhaps it could develop a force that would carry the water around. In other words, the rotational momentum of the bottle would dominate.
I see that you also tried dry sand. Didn’t that produce results similar to those of water?
Your comment about “pouring” the water in the half-filled case might be just what is needed to start thinking about a satisfactory explanation. But what about the trajectory of the center of mass of the water in the half-filled bottle? Why is this a different trajectory from that of the ice in the half-filled bottle? For example, at the moment of release, does the water stop contributing to the rotational momentum of the bottle? In particular, at that moment does the water drop out of the mass that contributes to the moment of inertia of the bottle and water system?
I would emphasize that this experiment demonstrates that a fluid with a low viscosity, such as water, will not react to a shear or sliding force acting on its surface. However, the same fluid will react to a uniform perpendicular force on its surface. A simple way we express this is “pressure.”
The rotation of the half-empty bottle is not transmitted to the water by the sides of the bottle. The water tends to stay put. It has not accelerated and it acts as a drag on the rotating bottle. When the full bottle is rotated, the water has no place to go if any force is applied on the surface of the bottle. The water will certainly try to remain in place, but the forces from rotating the bottle are transmitted as pressure to accelerate the water into rotation. When the water in the half-empty bottle is frozen, it behaves about the same as the empty and filled bottles. Forces are transmitted easily.
I learned a trick based on this same principles to tell the difference between a hard-boiled and a fresh egg without breaking them. You simply spin the egg. The hard-boiled egg spins easily like a top, but the fresh egg is sluggish. It stops rotating quicker than the boiled one.
This phenomenon is similar to that for the rotating bottles. The fluid in the fresh egg is viscous. It tends to stay put. There are two key factors. First, when the fresh egg is rotated by hand, the rotational force is not transmitted to the whole mass of the egg, because the fluid yields under shear force. Once you let go, the fluid in the egg acts as a drag on the rotating part of the egg.
This opens up the area of exploring different fluid viscosities.
This is generating a fascinating discussion! Yes, the idea of shear forces within a liquid certainly comes into play. Maybe that would be a good way to approach the explanation.
Great experiment! I like to think of the half-full experiment as trying to spin the bottle around the water, whereas in the other experiments the bottle and the contents rotate together.
Yes, this would probably be an excellent approach for the explanation—because in the half-full bottle, the water has some space. Nothing is holding it to the shape of its container once the bottle is released.
Did the discussion of the scientists create additional questions for you? Try to find answers to your questions by experimenting in different ways. Keep thinking about a satisfactory explanation that makes sense to you.
If you have any questions related to this activity, send them to us.
No one is perfect! Here are some outtakes to prove it!
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