deceleration & centripetal force

[michel123456]

Bob has showed a kitchen experiment, I will do the same.

This is small old video (sorry for the poor quality) of my casserole with cold water an reluctance of boiled salad (Greek speciality "horta").

Here we are: a small galaxy formation in my casserole.

 

Stupid, isn't it? Only that here we have deceleration, instead of the observed universe which accelerates. Bad analogy or something goes wrong?

[swaha]

what was the receipie? sorry dont mind!

[michel123456]

Evident lack of interest.

 

Rotating body. The rotational input ends, and the object collapses.

 

What happened?

[Sisyphus]

What happens in the video? (I'm currently on a computer that isn't mine for which youtube is blocked.)

[michel123456]

3 consecutive screenshots.

Casserole stands still.

Water is rotating counter clockwise by laboratorian through special ergonomic instrument (me with a wooden spoon), then the system is left to evoluate freely.

 

1.

 

2.

 

3.

[Sisyphus]

That's it? So you spin it, and friction/viscosity eventually brings it to a stop. The stuff floating on the surface gathers in the middle as per a standard vortex. What is it supposed to be an analogy for?

[michel123456]

That's it? So you spin it, and friction/viscosity eventually brings it to a stop. The stuff floating on the surface gathers in the middle as per a standard vortex. What is it supposed to be an analogy for?

 

Deceleration brings stuff together. Mass & deceleration creates centripetal force.

 

I supposed (maybe wrong) that if scientists agree on the existence of a BH in the center of a galaxy, that the galaxy was agglomerating (all the stuff gathers in the center) as in my casserole. Mass is agglomerating by simple Newton mechanics without any black Hole in the center (in my casserole). I only needed deceleration.

[Sisyphus]

The galaxy is not a soup, and stars are not floating on the surface of fluid. The galaxy is freely drifting matter, and the primary force at work is gravity. The soup slows due to viscosity, and the stuff floating on the surface is sucked in by the vortex of the stuff its floating on. I don't know what "deceleration brings stuff together" even means.

 

Also, the galaxy is not gathering stuff in the center, any more than our solar system is. We orbit the center, just like the Earth orbits the Sun.

Edited January 20, 2010 by Sisyphus

[swaha]

brother sisyphus is right. u cant draw analogy of universe with a soup i suppose. & i thought the universe was expanding so all galaxies r moving apart............. by the way what are the decelerating bodies in the soup? some leaves you eat?

[michel123456]

pissenlits

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Newton's first law of motion says: In the absence of a net force, a body either is at rest or moves in a straight line with constant speed.

When the body is rotating, there is no straight line. The rotating motion involves acceleration.

What is the natural motion of a freely rotating body?

[Sisyphus]

Depends on what you're talking about. A body that is merely rotating isn't accelerating as a whole - its center of mass isn't moving. Its parts are accelerating. So you have to look at the forces on, say, one molecule of a spinning top. And in that case there are lots of forces - intermolecular forces holding the whole thing together.

 

In the case of the solar system or the galaxy, what keeps the whole thing from just flying apart is gravity. That's the Newtonian force keeping the Earth constantly accelerating around in a circle around the Sun.

[michel123456]

I meant:

1. considering a leave in the casserole, when the center of rotation is outside the object, you have a system that acts like a sling http://en.wikipedia.org/wiki/Sling_(weapon) when you release the body, the leave goes following a straight line in the direction of the tangential vector.

In the soup experiment, the body is released but don't follow a straight line.

2. considering the soup as a whole, the center of rotation is inside the object, you have a system that acts like a non-rigid rotating object, a system I couldn't find any clear description of.

 

Taking the description of a rigid rotating body as a starting point : when released (without friction) would the rotating object conserve its angular velocity or not?

 

I don't know what "deceleration brings stuff together" even means.

The statement is true at least for linear motion. I have to find a gif I made sometime ago for explaining the opposite, that acceleration puts things away. It is simple vector addition.

[swansont]

You are not aware of the worldwide known

. (1) there was a thread about it on this forum.

 

(1) at the time i made it, i thought it was representing a spiral galaxy.

 

No, I was wasn't aware. But that doesn't change my statement; friction represents an external tangential force. Slowing rotation does not "give rise" to a centripetal force. Slowing rotation actually represents a decrease in the centripetal force, since F = mv^2/r

If v decreases, F decreases.

[michel123456]

Agree.

and when V gets to xero, F gets to zero too.

And as shown in the experiment, matter goes to the center. It is a visualization of a concentration process, without any modification of mass.

[Sisyphus]

No. Matter is not going to the center in that experiment. The stuff floating on the surface is going to the center.

 

Matter flows outward while it's spinning. The liquid climbs the edges of the pot (fighting gravity), and a depression develops in the center: a whirlpool. The inertia of the liquid tries to expand it, but the walls of the pot supply the centripetal force keeping it moving in a circle.

 

As friction slows it down, these forces decline. Their magnitude in relation to gravity decreases, and gravity once again evens out the level of the liquid.

[michel123456]

No. Matter is not going to the center in that experiment.

??

 

The stuff floating on the surface is going to the center.

That's what I ment.

 

Matter flows outward while it's spinning.

Yes. While spinning at regular rotational speed, or under accelerated rotation. And inward when decelerating.

 

The liquid climbs the edges of the pot (fighting gravity), and a depression develops in the center: a whirlpool. The inertia of the liquid tries to expand it, but the walls of the pot supply the centripetal force keeping it moving in a circle.

Yes.

 

As friction slows it down, these forces decline. Their magnitude in relation to gravity decreases, and gravity once again evens out the level of the liquid.

That does not explain why the stuff floating on the surface is going to the center.

[swansont]

That does not explain why the stuff floating on the surface is going to the center.

 

One should note that the floating stuff is less dense than the water, else it wouldn't float. So another way to ask the question is why the heavy stuff moves to the outside once the vortex gradient has been reduced, and I think that's a much more familiar problem.

[michel123456]

Actually, if you observe carefully the video, stuff don't float but stays at the bottom of the casserole. You'll notice that when the camera goes away for a moment & then goes back. The more dense goes to the center.

 

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and so is the Earth.

[Spyman]

Earth is not enclosed inside a huge container where stuff are affected by friction against the bottom or the walls.

[swansont]

Actually, if you observe carefully the video, stuff don't float but stays at the bottom of the casserole. You'll notice that when the camera goes away for a moment & then goes back. The more dense goes to the center.

 

Ah, well, I wasn't watching the video, I was going by your description above, where you asked why the stuff floating on the surface is going to the center.

 

Anyway, this sounded familiar, so I looked it up. It's called the tea-leaf paradox. The rotational flow isn't the only flow present in the cup.

http://explainers.wordpress.com/2007/10/05/tea-leaves-explained/

[Moontanman]

I know why the floating stuff moves to the center in a whirlpool... It's called gravity... the whirlpool effect causes the center to drop while the edges climb up the sides of the container this results in a down hill situation where anything on the surface falls to the center due to gravity. If you swirled a liquid in a container in zero G you would not see this effect, everything would cling to the outer walls of the container, gravity is responsible for the cone shape of the whirlpools as well as surface floaters sliding down to the center....

[michel123456]

I was not aware of the tea-leaf paradox. I use to drink coffee.

I think it has to do with vector decomposition. It is not a system in regular rotational motion. Since the system comes to a stop, it is accelerated (decelerated) rotational motion. Under regular rotation, the stuff is under acceleration caused by the change in direction. Under accelerated rotation, we are talking about acceleration of acceleration, in this case, deceleration of acceleration. Equations and vector analysis must exist somewhere, but i couldn't find anything about it.

 

I am gonna make the experiment in a large pool this weekend, to see whether the container walls play a role.

[michel123456]

I made the experiment. The walls do play a role.

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from wiki http://en.wikipedia.org/wiki/Tea_leaf_paradox

Explanation

Stirring the liquid makes it spin around the cup, causing a centrifugal force outward.

 

However, near the bottom and outer edges the liquid is slowed by the friction against the cup. There the centrifugal force is weaker and the pressure differences become more important for the water flow. This is called a boundary layer or more specifically an Ekman layer.[3]

 

Because of the centrifugal force, the pressure is higher along the rim than in the middle. If all the liquid rotated as a solid body, the inward (centripetal) force would match the outward (centrifugal) force from the rotation and there would be no inward or outward movement.

 

In a teacup, where the rotation is slower at the bottom, the pressure gradient takes over and creates an inward flow along the bottom. Higher up, the liquid flows outward instead. This secondary flow travels inward along the bottom bringing the leaves to the center, then up, out and down near the rim. The leaves are too heavy to lift upwards, so they stay in the middle. Combined with the primary rotational flow, the leaves will spiral inward along the bottom.[1][2]

 

_I don't see any mention of deceleration. Clearly, the "tea leaf" phenomenon appears when the input stops (when the spoon is taken out the cup and the system is left free).

[Sisyphus]

 

_I don't see any mention of deceleration. Clearly, the "tea leaf" phenomenon appears when the input stops (when the spoon is taken out the cup and the system is left free).

 

My guess about that is that it's got nothing to do with deceleration and everything to do with having a smooth enough flow for he currents to become dominant, which it can't settle into until after you've stopped stirring it with a spoon. By the time the leaves gather, it's already slowing to a stop, but the leaves aren't gathering because it's slowing. Just a guess.

[Spyman]

I think the spin speed has an significant influence, the rotation creates an artificial gravity were buoyancy will force submerged denser objects outward towards the wall.