I’ve got a bowl of soup. There are bits of seasoning, like bits of herbs, floating on top. When I turn the bowl, these bits stay in the same place, even if I rotate the bowl fast.
Is there a name for this phenomenon, and what is the explanation?
Inertia and low friction?
it’s the Soup Exception to Newton’s First Law
oil and fats are less dense than water. these molecules float to the surface of the watery broth giving the surface a sheen and provide lubrication.
“Inertia” pretty much covers it. The items you mentioned are at rest. To get them moving, you have to apply a force. If you spin the bowl, the viscosity of the soup will result in some force being applied to the mass of soup and ultimately to the objects floating on its surface - but it’s not much force, because the viscosity is very low. Still, it’s a non-zero force, and if applied for long enough - like if you put your bowl of soup on a record player and leave it spinning for a minute or so - everything in the bowl will eventually be spinning at the same speed as the bowl itself.
The same thing happens in reverse if you stop the record player: the bowl stops spinning immediately, but the soup inside will take a minute to come to a complete stop.
I wonder if you could use a bowl of soup as a low-tech navigational aid? Float a toothpick, say, on the surface of the soup pointing in a known direction (say, north). Then as you walk and turn, the toothpick continues to point north.
Obviously, hot soup would soon cool down, so I suggest starting with a cold soup. I intend to name this technology the Gazpacho Positioning System, or GPS for short.
Cute.
The reality is that viscosity-related drag will result in cumulative error over time - eventually, the toothpick won’t be pointing north. However, floating a magnet actually works quite well as a compass. Unlike friction between two sliding surfaces, viscosity drag scales with velocity - so as the magnet moves extremely slowly, the drag force falls away to nothing, and it points north quite accurately.
I predict you’ll eventually become hopelessly lost in the Arctic.
At least he’ll have some soup to eat.
For me, it’s ice cubes. Turn the glass and they barely move.
A long time ago, I was trying to get the ice cubes* in a glass I was drinking from to move so as not to obstruct my sips. Noticing that rotating the glass wasn’t getting the job done, I resigned myself to blowing the ice cubes to the other side of the glass. The person I was with asked, “Iced tea too hot to drink, is it?”
- Actually, if they had been cubes, it wouldn’t have been it a problem. They were those godawful crescents you get from ice makers, perfectly sized to block off the edge of the glass when drinking.
that’s where the expression, ‘off by a noodle’ came from.
What you should have done is left the glass in position and moved yourself around it.
:smack: It all seems so obvious now.
So if you put a spinning bowl on a treadmill. . .nah, forget it.
In all seriousness, the “Gazpacho Navigation System” is a crude form of inertial navigation, which is actually used in real instruments. Just using devices a bit fancier than a bowl of soup.
That was the other example I thought about using, but I was already eating soup at the time.
I hate those things. But there’s no alternative in the automatic ice making game anymore. I’ve asked around and *nobody *makes a non-crescent ice maker; apparently it’s just the most reliable design. So I never connected the ice maker in my new fridge; I’ve got a set of the BIG ice cube trays, and I’m considering buying that thing that makes the big spheres.
I remember solving a similar problem in my senior fluid mechanics course. You are describing a transient behavior, if you keep spinning the bowl : eventually the surface layer will spin with the bowl (Solid-Body Rotation) and the surface will take on a parabolic shape.
Here are some links to illustrate :
1> [http://paoc.mit.edu/labweb/notes/chap6.pdf](The equations of fluid motion) - See page 179 to page 180 for a picture of a large spinning rectangular tank with water at steady state.
2> Here is a link showing the dynamic nature of the solution : it gives the Rayleigh problem solution of a fluid in rotation in terms of the Complementary Error Function. You will see that depending on how deep the bowl is - the surface can take minutes to hours to reach the steady state.
3> Here is a third link showing the same equations as in bullet 2. (Bullet 2 equations may not show correctly in your browser).
I’d also like to point out that the above solutions are for Newtonian fluids - water, air etc. Your soup will probably behave in a non-newtonian manner (depends on what you have in the soup) and the equations will need to be modified.
One practical application of this is the large liquid metal (mercury or gallium) spinning telescope mirrors that astronomers use. Here is a youtube video from NASA. Here are the design details of a liquid mirror telescope.