# What keeps the cookie in my coffee from moving when I rotate the cup?

I dropped a browny cookie in my coffee cup, it sank at first but then surfaced after a couple of minutes. I tried to rotate the cup to lure the cookie out, but it got stuck in place.

Please check out the video below and tell me what keeps the cookie from moving?

• Aliens, obviously!! Dec 10 '20 at 16:22

The low viscosity of the coffee means that you can rotate the cup without significantly moving the liquid it contains: there's simply not enough friction to 'drag' the liquid by the cup's wall.

It would be a different picture with a viscous liquid like oil or runny honey.

It's useful to remind us what Newtonian viscosity $$\mu$$ really is.

(Source)

For $$\mu \approx 0$$ then $$\tau \approx 0$$, so there isn't enough shear stress (friction) to make the liquid content of the cup rotate.

Of course the answers like 'it is because of low viscosity' are good, but it is also nice to overcomplicate this problem.

### You are not rotating the cup

The cookie does rotate/move in some sense but only slightly. The reason that the cookie is not rotating a lot is that you are actually not rotating the cup. Instead, you are giving the cup a short twist, which is a short acceleration of the cup and then a short deceleration of the cup. If you would make the cup rotate continuously then the cookie would eventually approach the situation to move with the same speed as the cup.

### Correlation between movement and force

You can interpret the 'why does the cookie not move/accelerate' as 'why doesn't the cookie move/accelerate simultaneously with the force that I apply to the cup'. An interesting analogy (and the reason why I post this viscous answer) is in dynamic mechanical analysis that use oscillatory stress to determine the viscoelastic behavior of materials.

If you would oscillate your motion in a regular pattern then you get that the cookie will also oscillate. How much and in what way it oscillates will depend on two factors:

• How much will depend on the complex modulus. The ratio of the force applied to achieve some deformation and the amount/amplitude/size of the deformation.

• In what way will depend on the viscoelastic behaviour of the material. For liquids, you get that the force is related to the inertial force and the acceleration of the cup and its contents (which is highest in the middle of the oscillation when the speed is higher). For elastic/solid materials you will get that the force is related to the elastic force and it will be high at the end points of the oscillation.

(of course you get as well acceleration of the cup which is elastic/solid, but imagine that the coffee cup is a plastic cup with negligible weight)

So you can get the cookie to move/oscillate, but you just need to apply a large enough force because you have a material with a low complex modulus (whether it is liquid matter or not does not matter).

What makes it intuitively strange that the cookie does not rotate is a psychological effect:

• You have to apply a large force.

This large force is necessary to move the heavy cup.

If you would be moving a very light plastic up and apply the same force or power then you would make the liquid and cookie move much more. Or, for the same movement of the cookie you would need much less force.

• What do you think will happen if I move the cup forward(let say 20 CM)? Will the cookie stay in its relative place in the cup, or will it stay in its relative place in the room and crash into the cup side as it moves? Dec 9 '20 at 18:29
• I am not sure what you mean by CM but if you keep turning the cup then eventually the cookie should start to rotate with the same speed as the cup (theoretically it will be nearly the same speed because air friction will cause the cookie to rotate slightly slower, you also get a lot of secondary flows due to initial instabilities like here). Dec 9 '20 at 19:38
• TL;DR the world is complicated, physics is hard. Dec 9 '20 at 19:44
• @SextusEmpiricus CM=centimiters, sorry. I meant what will happen if instead of a rotation I will move the cup forward in a straight line. Will the cookie remain in its relative position to the cup, or will it move? Dec 9 '20 at 19:50
• @Ilya Gazman, you might indeed expect that with a translational movement the cookie remains in place relative to the cup with a translation. This is also what happens to some extend if the movement is not too fast acceleration, in which case the cookie won't bounce against the wall of the cup. You also might have heard of the idea of survival in high drops from a waterfall where the surrounding water prevents the body from crashing... Dec 10 '20 at 8:06

The water does not rotate with you cup because water is liquid. water touching the cup moves a little bit but not the water away from the cup. the friction between different molecules of water is very small.

Another way to view viscosity is as a kind of "momentum conductivity". Just as a thermal insulator, with low heat conductivity, transfers heat only slowly (though faster the bigger the temperature difference), a low viscosity fluid transfers momentum only very slowly (though faster the bigger the momentum difference). (It works mathematically for sideways/shear momentum anyway, and maybe other types.)

Rigid solids like what the cup is made of are very high-viscosity by definition: Push on any part with your hand and the momentum spreads throughout the whole solid almost immediately (at speeds related to the P- and S-wave speeds of sound I suspect). The coffee on the other hand is low viscosity, so, although a small amount of the rotation is very slowly getting to the cookie, it's so slow you barely notice in the video.

As Kian Maleki alluded to, the microscopic origin of viscosity comes from the forces between molecules (or atoms or ions). Gasses can only transmit momentum through collisions, which leads to very low viscosities; liquids have both constant pushing and constant pulling forces on each other, but still easily slide past each other without fully transmitting momentum, leading to medium viscosities; and solids have strong forces holding the molecules in their particular arrangement that takes a lot of force to change, leading to extremely high viscosities.

• Actually, it is possible to have a liquid with a lower viscosity then a gas, e.g. if that liquid is superfluid helium. I'm not sure it's possible to have a liquid with a higher viscosity than a solid, but it seems likely that it could at least arguably happen, just definitely not in your situation. Dec 9 '20 at 6:31
• Maybe if jello is a solid and pitch is a liquid, then pitch is a liquid that's less viscous than the solid jello in terms of viscosity being momentum conductivity. I don't know if that's really true or makes sense, though. Dec 10 '20 at 0:22

When you move the cup , there are weak adhesive forces operating between liquid and mug due to which the liquid can be treated as a separate object which isnt rotating

Since we see that the cookie sank and ultimately rose due to buoyant force . This cookie is in a medium which itself is at rest so there is no reason for it to move, rotate