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In a non-planetary circular orbit, where centripetal force is given by the contact with the rotating tube wall instead of gravity, why does a heavier object tend to move in a larger orbit?
For instance, when you have solid suspended within water, the solid particles, which is heavier than water molecules, move outwards and accumulate along the inner tube wall, while the lighter water molecules keep moving in the smaller orbit, staying closer to the centre than those particles.
How can you express why objects with higher mass move in larger orbit?
As the object move outwards, the radius increases but the velocity also increases (when you spin a circle, the point near the centre moves slower than the edge).
Different mass, different velocity, different radius, and different force. I'm just not sure how the whole thing works.

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closed as unclear what you're asking by John Rennie, stafusa, Bill N, Kyle Kanos, Jon Custer Oct 3 '17 at 13:40

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  • $\begingroup$ Are you asking how a centrifuge works? $\endgroup$ – sammy gerbil Oct 2 '17 at 9:29
  • $\begingroup$ Yes..I'm having trouble understanding the relationship between velocity and orbit radius as mass changes, because in a centrifuge more massive objects move outwards, which has larger orbit but also faster velocity. $\endgroup$ – Chris K Oct 2 '17 at 13:03
  • $\begingroup$ See DavidZ's answer at physics.stackexchange.com/questions/1888/… $\endgroup$ – Bill N Oct 2 '17 at 17:46
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    $\begingroup$ Possible duplicate of Balloons and lifting gases $\endgroup$ – Bill N Oct 2 '17 at 17:47
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Imagine yourself in front of a cup of tea.

You notice that there are tea leaves in the cup (that came out of a hole in your teabag). Some lighter leaves seem to float on top of the surface, while some heavier ones have gathered at the bottom. You shrug it off, and take a spoon of sugar and put it into the tea and start stirring it. You now notice that the tea leaves which were initially floating randomly now seem to have gathered at the center of your cup, while the ones at the bottom have gathered around the edge.

(In fact you can try this experiment with things simple as water and pieces of plastic or oil drops and tiny pebbles or beads!)

And now you start thinking.

Initially, the leaves were at the top, while the water was a the bottom. Surely that must be because the tea leaves are "lighter" than water. But what we actually mean by "lighter" is less dense.

But what does it being less dense than water have to do with the fact that its at the top?

Water is a fluid. And fluids have a tendency to flow; to flow to whatever direction they feel a tug(force). This causes them to exert pressure (force on the surface area) on objects in contact with it and this in turn causes buoyancy, which Archimedes has beautifully taught us to interpret.

Hence if the object in question is less dense than the fluid in question, then it will be pushed around by the fluid to a place where the fluid will least want to go, and vice-versa.

When you stir the cup of tea, what happens is you give the water molecules a rotational kinetic energy; they start revolving around an axis, the center of the cup.

Now, looking at the system from a non-inertial frame of reference where the rotational velocity is zero, all the particles must have a pseudo force acting on it. That force is always directed towards the axis of rotation.

The net force on all the particles is oblique. The water wants to go to the bottom center, so do the tea leaves.

If you haven't figured out by now, applying the same logic of buoyancy, we get our answer. The water will push the lighter leaves to the top and to the edge of your cup, while it is unable to do so for the heavier tea leaves, which then dominate and stay at the bottom center.

I hope I answered your question, and also cleared your doubts. Your doubt had little to do with rotational kinematics and more to do with buoyancy. It is wrong to assume that solids are always heavier than liquids. And that solids will always sink in liquids.

P.S. First post. Yaaay! ;)

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  • $\begingroup$ How would this apply in a case of suspended gas molecules? For instance if you have U-235 and U-238 mixed together, and spin the tube containing them and end up with U-238 accumulating along the edge. Apparently it's because objects with higher mass tend to move at larger circular orbit; but why is it so? Why do heavier objects move at larger circular orbit? I know it sounds quite intuitive but I can't really express in physics equations. $\endgroup$ – Chris K Oct 1 '17 at 20:09
  • $\begingroup$ You are still confused between the notion of density, mass and weight. A kilogram of foam sheets, or a kilogram of gold, which one would weigh more? Both would weigh the same! But now put both in water. The gold sinks, while the foam floats. The foam also occupies much more space than the gold, it is less dense. Isotopic separation works on the principle of Graham's Law of Diffusion, and not directly on rotational dynamics. $\endgroup$ – Debaditya Oct 2 '17 at 7:24
  • $\begingroup$ But we can still attempt to look at the scenario. U238F, and U235F, here both of these are gasses, but due to different isotopes of U, U238 is heavier than U235, by 5amu per molecule, or 5 grams per mole, while occupying the same space, hence U238 is more dense than U235. $\endgroup$ – Debaditya Oct 2 '17 at 7:26

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