[PmbPhy]

...... and here's a paradox for those interested in such things..... if the inward and outward forces are identical, there is no net force inward, so the stone doesn't move in a circle after all!
/quote]
That is an invalid deduction. Zero radial force means zero radial acceleration. From an inertial frame, if an object is moving in a circle then the outward force is balanced by the centripetal force. That doesn't mean that all other forces are zero. Acceleration is a vector quantity and the acceleration vector is non-zero since the object is not moving in a straight line.

Buy the way. I forgot to mention that in a rotating frame the Coriolis force is non-zero and is a velocity dependent force. Centripetal force is the radially inward force acting on body to make it move in a circle.

[alancalverd]

I wish there was a "tongue in cheek" emoticon, but Nemesis Pete is just as effective!

[rmolnav]

"Ah, but if you cut the string, the stone doesn't fly away from the center!" Oh yes it bloody does. Tangentially, not radially, but still away from the center (assuming that you and I share the definition of "away").

I´ve long been defending the existence of real centrifugal forces ("real" meaning they produce physical effects), and many times have seen stuff similar to what quoted  ...
But I´m afraid your approach isn´t fully correct.
Whatever definition we give to "away", that tangential movement has NOTHING TO DO with any centrifugal force, because, since the very moment you cut the string, both centripetal and centrifugal force DOESN´T EXIST any more ... Therefore, the stone keeps the velocity vector it has at that moment ! (Newton´s First Motion Law).
 

3. Every action provokes an equal and opposite reaction, so the tension pulling the stone inwards is balanced by the force I feel pulling my hand outwards

Newton´s Third Motion Law doesn´t actually say " Every action provokes an equal and opposite reaction" ... Though First and Second Laws refer to a single object, Third Law refers to TWO objects, and mentioned "action" and "reaction" forces are exerted by each of them ON THE OTHER !!
And your phrase " ...the tension pulling the stone inwards is balanced by the force I feel pulling my hand outwards" deals with THREE objects: stone, string and your hand ...
You have to analyse each directly interacting pair separately.
1) Outer string end has to exert an inward force (centripetal), to "bend" stone trajectory ... Due to inertia phenomenon, the stone exerts an outward force (centrifugal, in its ample sense) ON THE STRING END ... "Net force inward" doesn´t become null whatsoever: to add force vectors applied on different objects has no sense at all !!
2) To produce above mentioned centripetal force on the stone, the string has to be tight ... YOU have to pull inwards the inner end of the string: centripetal force exerted on that end OF THE STRING ... As a reaction the string exerts an outward force ON YOUR HAND (the one you certainly feel).
And those two pair action/reaction forces, though being each pair equal but opposite, have different sizes. Apart from friction energy wasted, the string is also rotating and requires a "net" inward force exerted on it: your pull on inner end the string has to be bigger than the outward pull of the stone on outer end of the string ...
QUITE ANOTHER thing is the question of inertial "effects" on the accelerated object ITSELF ... The stone internally "feels" is being accelerated, and internal stresses do appear ... If the stone is connected to the string through a hook on its surface, those internal stresses are tensile. But in the case of a sling, they are compressive, quite the opposite.
Even more "tricky" is the case when, instead of a "physical" connection such as a string, it is the gravitational pull of another massive object what exerts as centripetal force and "forces" the first object to bend its trajectory ...
That´s what I´ve long been discussing on "Why do we have two high tides a day", as I said here a couple of days ago ...
It is very interesting what linked by PmbPhy,  http://www.newenglandphysics.org/physics_world/gr/inertial_force.htm
As I´ve said several times I think inertia, and frames of reference "tool", are rather misunderstood/misused by many. But I need further "rumination" on the lot of things said on that link, before any other comment.

[alancalverd]

Whatever definition we give to "away", that tangential movement has NOTHING TO DO with any centrifugal force, because, since the very moment you cut the string, both centripetal and centrifugal force DOESN´T EXIST any more ... Therefore, the stone keeps the velocity vector it has at that moment ! (Newton´s First Motion Law).

If it moves away when I cut the string, the string must have been exerting some force on it before the cut.

[rmolnav]

Whatever definition we give to "away", that tangential movement has NOTHING TO DO with any centrifugal force, because, since the very moment you cut the string, both centripetal and centrifugal force DOESN´T EXIST any more ... Therefore, the stone keeps the velocity vector it has at that moment ! (Newton´s First Motion Law).

If it moves away when I cut the string, the string must have been exerting some force on it before the cut.

Come on ! That´s obvious ...
But, on the one hand, what you had previously said is that movement "away" should be due to a "centrifugal" force ... Now you say "the string must have been exerting some force on it before the cut" ... But the existence of that force, which is "centripetal", doesn´t prove the existence of any centrifugal force moving "away" the stone ...
On the other hand, what that force (certainly existing before the cut) actually does is ONLY to make the stone get the velocity vector it has at the moment when the string is cut ... Neither a centripetal force, nor (and "let alone") a centrifugal one is acting on the stone after the cut ... As people now say "we are now on another screen" ... And the stone just continues straight and at constant speed, the way inertia manifests itself when no force is exerted on massive moving objects (not considering stone weight and air friction, what initially have only small curving effects).

[David Cooper]

I've only just found this thread - I rarely find enough time to explore the forum beyond looking up new replies to threads I've posted in.

But ...... and here's a paradox for those interested in such things..... if the inward and outward forces are identical, there is no net force inward, so the stone doesn't move in a circle after all! The inward force must exceed the outward force! Free energy, perpetual motion, collapse of Newtonian physics......

This relates to something that's been bothering me.

If you have a ball on a string going round some relatively fixed point to which it's tied, centripetal force is generated in the string in one direction while "reactive centrifugal force" (the only real kind of centrifugal force) is generated the opposite way in the string.

If we have two objects of equal mass on opposite ends of a string which are going round each other, the string then has both centripetal and reactive centrifugal forces running through it in both directions in equal amounts.

If the forces in opposite directions through the string are equal though (and we can see very clearly in this example that they should be), how do the objects follow circular paths instead of moving along straight lines? In the case of the single ball case where the other end of the string's attached to a fixed point, you can imagine that the forces are equal when analysed in a rotating frame, but not equal when analysed from a non-rotating frame, but that doesn't look possible in the case with the two balls of equal mass both going round in circles on the same path - in the analysis from a rotating frame, the forces each way through either end of the string can be considered to be equal, but it looks as if the same must apply when you analyse it from a non-rotating frame.

Is it somehow possible for the forces only to be equal in the middle of the string but not equal towards the ends so that the balls don't follow straight lines?

[rmolnav]

Is it somehow possible for the forces only to be equal in the middle of the string but not equal towards the ends so that the balls don't follow straight lines?

Leaving aside the questions of the generation of the rotating "scenario" and what relative to frames of reference (long discussed on the other thread), I think you´re making an error similar to what I told "alancalverd" « on: Yesterday at 11:49:10 »
The balls would follow straight lines if two equal but opposite forces were being exerted on each of them ... But what actually happens at both string connections to the balls is that string exerts the centripetal force ON THE BALL, and each ball exerts the centrifugal force ON THE STRING END ... (Third Newton´s Motion Law).
Therefore, on each ball only a centripetal force is applied ...
But, as I said yesterday:

QUITE ANOTHER thing is the question of inertial "effects" on the accelerated object ITSELF ... The stone internally "feels" is being accelerated, and internal stresses do appear ... If the stone is connected to the string through a hook on its surface, those internal stresses are tensile. But in the case of a sling, they are compressive, quite the opposite.

.
And if e.g. the balls were wet, with water on their surface, that water would "feel" a centrifugal force that, despite surface tension, would make the water move towards outer sides of the balls ...
All that occurs in a way very similar to what happens on earth, due to its revolving around moon-earth barycenter. Though in earth case water also  "feels" other forces: pretty constant own weight, and variable moon´s gravitational pull, and ALL mentioned forces cause moon-related tides ...
By the way, ALL THAT has nothing to do with reference systems: it can be seen whatever the observer is rotating with the balls, with the earth, with the moon ... or from an independent spaceship !!

[David Cooper]

The balls would follow straight lines if two equal but opposite forces were being exerted on each of them ... But what actually happens at both string connections to the balls is that string exerts the centripetal force ON THE BALL, and each ball exerts the centrifugal force ON THE STRING END ... (Third Newton´s Motion Law).
Therefore, on each ball only a centripetal force is applied ...

That's what I was missing. Thanks. So the two forces are absolutely equal at any point along the string (but both slightly higher towards the centre). It's in the rotating frame then that the centrifugal force is calculated as acting on the ball to push it outwards as much as it's being pulled in, but that's a radically different approach - I was mistranslating between the two.

[alancalverd]

So if I spin a blood sample in a "centrifuge", what makes the denser elements move outwards? It can't be the effect of a centripetal force pulling the lighter liquid inwards, because you can't pull a liquid.

[rmolnav]

So if I spin a blood sample in a "centrifuge", what makes the denser elements move outwards? It can't be the effect of a centripetal force pulling the lighter liquid inwards, because you can't pull a liquid.

That case is kind of similar to the sling case, where due to the fact that the stone is PUSHED inwards by the string loop (centripetal force), the stone also PUSHES the string loop outwards (centrifugal force), and the stone is "compressed" internally.
The centrifuge container "forces" outer blood layer to turn (thanks to friction), and that is transmitted inwards layer to layer ... Between two contiguous layers Third Newton´s Motion Law also applies, and inner layer PUSHES outer one outwards (centrifugal force), what increases pressure, the outer the more ... ALL blood elements tend to go outwards, but denser ones "win" the battle, and they move outwards, not letting lighter ones do the same ... (similarly to the static case where denser elements go down, and lighter ones up).
Initially it´s the same reason why in a cylindrical container filled with a not homogeneous liquid, if spinning round its vertical axis, liquid surface gets an inverted paraboloid shape: liquid  pressure horizontally increases, the outer the more, and denser elements "concentrate" at outer bottom zones ... But the centrifuge is suitably perforated, and denser elements go out first and get separated from lighter ones.

[rmolnav]

Initially it´s the same reason why in a cylindrical container filled with a not homogeneous liquid, if spinning round its vertical axis, liquid surface gets an inverted paraboloid shape

In the case of a non homogeneous liquid such as blood, surface shape is similar to a paraboloid, but not exactly equal, as can be seen below.
To add some maths to what quoited, you can have a look at what some time ago I sent to another s science-related blog:
"Let us imagine the cylinder of water inside the spinning bucket broken up into a number of telescopic pipe-shaped volumes of water.
Certainly water at the bigger of those volumes, in contact with the bucket, just tries to keep constant its speed vector, value and direction (Newton´s 1st law).
But the bucket makes it impossible, exerting an inward pressure that causes centripetal forces for the rotation.
And due to Newton´s 3rd law, the water exerts an outward, centrifugal reaction force.
Something similar to that can be said about the interaction between that bigger, most outer pipe-shaped volume, and the inner contiguous one ... and so on up to the axis of rotation.
On each “pipe” two opposite forces (pushes) are exerted: one by outer contiguous pipe (centripetal), an another by the inner contiguos pipe (centrifugal). First one has to be bigger than second one, in order to have a net centripetal force to make that water rotate.
On the one hand, centripetal acceleration has to be equal to the angular speed to the square, multiplied by the radius (ω²r). Then, it is proportional to the radius.
On the other hand, as f=ma (Newton´s 2nd law), the force “f” has to be also proportional to mass “m”.
But “m” is proportional to volumes (watch out: ONLY if uniforme density, as with water: NOT in the blood case). Let us consider 1 cm high horizontal slice of that "telescopic device”. Volumes are proportional to the square of the radius.
So, centripetal force is proportional to the radius to the cube (exponent 3 equal to 1+2, proportionality due to acceleration + prop. due to mass).
But in Fluid Mechanics pressure is paramount value, force divided by surface.
As vertical surfaces of those 1 cm telescopic slice water “rings” are proportional to their radius, “centripetal” pressure has to be proportional to the square of the radius (exponent 3 due to proportionality related to force minus 1, due to proportionality related to surface).
But in liquids that pressure, in a given point, is the same whatever the orientation of the considered surface. When in a dynamic equilibrium, the weight of a vertical water column of 1 cm2 section, from a given point to water upper surface, has to be also proportional to the square of the radius.
So, that column of water has to have a hight proportional to the square of the radius ... : the shape of a paraboloid !"
And that physical phenomenon offers different possibilities to practically separate  denser particles in a centrifuge from lighter ones ...

[rmolnav]

I´m going to size the opportunity that the "centrifuge" case, as explained on my last posts, gives us ... What for? To explain why many times I´ve said the question of inertial and not inertial frame of references are erroneously used by many (at least in a misleading way). E.g.:

Quote from: jerrygg38 on 14/08/2016 19:21:31
What is centrifugal force?
It´s the force on an object resulting from observing the object in a rotating frame of reference.
Quote from: jerrygg38 on 14/08/2016 19:21:31
In the previous discussion Alancalverd stated that there was no such thing as centrifugal force.
That's because he uses a definition of force which applies only in inertial frames.

you can imagine that the forces are equal when analysed in a rotating frame, but not equal when analysed from a non-rotating frame

Even knowledgable people consider we have always to add the phrase "relative to a non-inertial frame of reference", if we mention "centrifugal force". And they even add the adjective "fictitious", and think no centrifugal force is real ...
In the case of the centrifuge, and in many others, we can see REAL inertial effects such as the increase of pressure proportionally to the square of the distance from the axis of spinning ... WHATEVER the frame of reference ...
And that increase of pressure only can be due to the existence of both centripetal and centrifugal forces, the former due to the fact that some energy source is making the bucket rotate, and the later REAL inertial forces (as explained on my last posts).
Let us imagine  a huge cylindrical bucket, with a vertical shaft along its axis, and with a seat  on top.
If it is partially filled with water and made spin, for an observer on the seat, after some transient situation (friction needs time to make all water spin ...)  APPARENTLY there would be no rotation, because it´s the case of a so called "non-inertial" reference system ...
If "no" rotation, no centripetal acceleration is required, and no manifestation of inertia such as centrifugal force could "exist" ...
But still, he is seeing water surface changes from flat into a paraboloid !!
In that "artificial" scenario, he can´t explain what happens ...
"It´s easy", physicists say ... If you apply "fictitious!" outward forces (equal to ω²r per unit of mass, being ω the angular speed of rotation of the "observer"), you have a "sound" scenario (the adjective is mine) and you can make any calculation using that "non-inertial" frame of reference !!
I do understand there are cases where those rotating frames of reference can be useful for calculations, but to say centrifugal force ONLY can be that "fictitious" one, and always related to the chosen system of reference, is utterly erroneous ...
At least in the analyzed case, Logics leads me to say quite the opposite: "suppressing" the rotation (relatively to the "rotating" frame of reference), requires the application of "fictitious" centrifugal forces ... precisely the REAL ones which "previously" existed, and have disappeared relatively to the non-inertial frame of reference !!

[David Cooper]

You quoted me saying "you can imagine that the forces are equal when analysed in a rotating frame, but not equal when analysed from a non-rotating frame" in your last post, and I want to comment on that. It refers to the case of a ball on the end of a string going round in circles, the other end of the string fixed to something that doesn't move.

With the rotating frame, there's an imaginary centrifugal force pulling the ball one way and centrifugal force pulling it the other way, and these two forces are equal, so the ball stays the same distance from the centre.

With the non-rotating frame, there's no centrifugal force pulling the ball in the opposite direction from the centripetal force. What we do have though is reactive centrifugal force opposing the centripetal force in the string, and they are again equal in strength.

Going back to the rotating frame, the centripetal force in the string must also be opposed by an equal and opposite force, and this job is presumably imagined to be done by the imaginary centrifugal force instead of by reactive centrifugal force, so the centrifugal does the same job as reactive centrifugal force while also trying to accelerate the ball away from the centre.

In reality, rotating frames are an abstraction, and the result of using that abstraction is that imaginary forces come into play that don't exist in reality (or where part of their role is real but the other part is fake). All the things in nature that are imagined to be centrifugal force must actually be the real force called reactive centrifugal force which merely opposes centrifugal force. If we have a mouse clinging to a hamster wheel and spinning round inside it very fast (after it stops running suddenly), the rim applies centripetal force inwards against the mouse (applying pressure to it), and the reactive centrifugal force is where the mouse presses back against the rim of the wheel. With the ball on the string, the centripetal force is applied as a tension from the other side, and the reactive centrifugal force is also applied as a tension in the opposite direction. In a centrifuge, we have a case like the mouse in the wheel rather than a ball on a string, but we're still dealing with the real force called reactive centrifugal force, and that force only ever exists as a reaction opposing centripetal force. No one should be rejecting the existence of reactive centrifugal force, and no one should be asserting the existence of centrifugal force of the other kind because it is only an artefact of an abstraction - it is the latter kind that has been rejected by science, and the two should not be mistaken for each other.

[Vasyl]

No one should be rejecting the existence of reactive centrifugal force, and no one should be asserting the existence of centrifugal force of the other kind because it is only an artefact of an abstraction - it is the latter kind that has been rejected by science, and the two should not be mistaken for each other.

The more I read, the less I understand. Could you please help me to understand one thing: Is it possible to accelerate a particle (like in Hadron Collider) in a closed system, for example in a deep space?

[rmolnav]

No one should be rejecting the existence of reactive centrifugal force, and no one should be asserting the existence of centrifugal force of the other kind (??) because it is only an artefact of an abstraction - it is the latter kind that has been rejected by science, and the two should not be mistaken for each other.

I´m not going to continue to discuss with you some "details" we have long discussed on the "tides" thread, to no avail ...
But please kindly note that you can find definitions of "centrifugal force" considering it ONLY as a "fictitious" force ...
E.g.,  on "Britannica.com", certainly with physicists as technical advisers, the definition is just:
"Centrifugal force, a fictitious force, peculiar to a particle moving on a circular path, that has the same magnitude and dimensions as the force that keeps the particle on its circular path (the centripetal force) but points in the opposite direction".
Though, curiously, further down they themselves give links to other britannica articles, among others precisely the "centrifuge" one where you can read:
"Centrifuge, any device that applies a sustained centrifugal force—that is, a force due to rotation. Effectively, the centrifuge substitutes a similar, stronger, force for that of gravity. Every centrifuge contains a spinning vessel; there are many configurations, depending on use. A perforated rotating drum in a laundry that throws off excess water from clothes, for example, is a type of centrifuge. A similar type is used in industry to separate fluids from solid matter after crushing",
and, logically, that "centrifugal force" has to be REAL ... They just say "due to rotation", without any reference either to centripetal force (the one exerted by the spinning vessel on the liquid to make it follow a circular path), or to the inertial outwards reactive forces exerted by the liquid, both internally between cylindrical layers of liquid, and on the inner side of the vessel ...
And those forces are "centrifugal" and real: otherwise pressure would not increase outwards, as explained on my last posts !!
By the way, what happens in the centrifuge case in some aspect is similar to what in the case of a ball being made rotate with a sling, "pushing" it inwards (on its outer side), instead of "pulling" from a hook on its inner side (as when hammer throwing) ... The sling rotation (together with inertia) produces compressive forces inside the ball, the outer the more, as in the centrifuge the vessel spinning and inertia cause the increase of pressure, the outer the more too !!

[David Cooper]

No one should be rejecting the existence of reactive centrifugal force, and no one should be asserting the existence of centrifugal force of the other kind because it is only an artefact of an abstraction - it is the latter kind that has been rejected by science, and the two should not be mistaken for each other.

The more I read, the less I understand. Could you please help me to understand one thing: Is it possible to accelerate a particle (like in Hadron Collider) in a closed system, for example in a deep space?

Why wouldn't that be possible, and why are you relating that to centrifugal force?

[Vasyl]

Why wouldn't that be possible, and why are you relating that to centrifugal force?

If it is possible than we can create artificial "asteroids" and attach a spaceship to them to explore space. Or is it not possible?

[David Cooper]

No one should be rejecting the existence of reactive centrifugal force, and no one should be asserting the existence of centrifugal force of the other kind (??) because it is only an artefact of an abstraction - it is the latter kind that has been rejected by science, and the two should not be mistaken for each other.

I´m not going to continue to discuss with you some "details" we have long discussed on the "tides" thread, to no avail ...

The problem there was that you wanted to have some kind of centrifugal force involved in cases where the centripetal force is gravity, but there is absolutely no centrifugal force of any kind involved in that other than in the abstraction of rotating-frame analysis.

But please kindly note that you can find definitions of "centrifugal force" considering it ONLY as a "fictitious" force ...

Inadequate definitions exist all over the place, but we don't need to trip over them. The whole point of working to acquire a deep understanding of the physics in places like this forum is to become better able to tell whether what you're reading is correct or faulty. Often the faults are in omission where someone has written something with only one thing in mind and hasn't thought to clear up other issues, in this case because of an ambiguity. Different contributors to an encyclopaedia can use ambiguous words in different ways, all intending to provide good information (and doing so if you read them the right way), but the different ways in which they word things can appear to produce contradictions.

Though, curiously, further down they themselves give links to other britannica articles, among others precisely the "centrifuge" one where you can read:
"Centrifuge, any device that applies a sustained centrifugal force—that is, a force due to rotation.

You're first Britannica quote dismisses centrifugal force entirely (because the writer is only thinking about the fictitious kind of centrifugal force of the kind that provides the illusion of existing in rotating frames), but your second one which refers to a sustained centrifugal force is actually talking about reactive centrifugal force which is a real force - it is just referred to in a more economical way (by missing out the word "reactive") that depends on the reader applying correct understanding to it. That way of wording things is the standard way of doing so when talking about a centrifuge. It is your job to catalogue the information correctly in your head, filing it under "reactive centrifugal force" rather than "centrifugal force".

and, logically, that "centrifugal force" has to be REAL ... They just say "due to rotation", without any reference either to centripetal force (the one exerted by the spinning vessel on the liquid to make it follow a circular path), or to the inertial outwards reactive forces exerted by the liquid, both internally between cylindrical layers of liquid, and on the inner side of the vessel ...

Your understanding of physics should enable you to link the thing they're calling "centrifugal force" to the correct real phenomenon and not to be misled into thinking there is some other centrifugal force involved in the situation.

And those forces are "centrifugal" and real: otherwise pressure would not increase outwards, as explained on my last posts !!

The centripetal force is higher further out, and the reactive centrifugal force goes up to match that - the thing being called centrifugal force in a centrifuge is the reactive force responding to the centripetal force.

By the way, what happens in the centrifuge case in some aspect is similar to what in the case of a ball being made rotate with a sling, "pushing" it inwards (on its outer side), instead of "pulling" from a hook on its inner side (as when hammer throwing) ... The sling rotation (together with inertia) produces compressive forces inside the ball, the outer the more, as in the centrifuge the vessel spinning and inertia cause the increase of pressure, the outer the more too !!

And I suppose you think I didn't say that in the post you're attacking. Note where I talk about tension and pressure in relation to how the centripetal force is applied. Ball on string --> tension; mouse in hamster wheel --> pressure.

[David Cooper]

Why wouldn't that be possible, and why are you relating that to centrifugal force?

If it is possible than we can create artificial "asteroids" and attach a spaceship to them to explore space. Or is it not possible?

Are you sure you're posting in the right thread? Why would you want to handicap a space probe by tying an artificial or real asteroid to it? The less mass (other than fuel) that you have to accelerate, the easier it is for the probe to go exploring, and the higher the speed you'll get it to.

[rmolnav]

your second one which refers to a sustained centrifugal force is actually talking about reactive centrifugal force which is a real force - it is just referred to in a more economical way (by missing out the word "reactive") that depends on the reader applying correct understanding to it.

As I´ve already said, it´d be useless to continue here our so long discussion
on the thread about tides ...
But I want to repeat I don´t agree with some of your "basic" dynamics ideas, e.g., what quoted ...
Centrifugal forces, the ones really acting in nature, are always manifestations of inertia when physical objects are accelerated "centripetally" (therefore, moving along a curved trajectory), whatever the essence of the required centripetal force and rest of circumstances.
The "fictitious" ones only "exist" inside our minds, when we use rotating frames of reference for our calculations ... In that "virtual" scenario, as actually rotating objects kind of "stop" their rotation (--> no centripetal acceleration and no inertial effects), we "need" to introduce a "fictitious" external centrifugal force, that causes effects IDENTICAL to the ones actually caused by the sheer fact of the kind of "hidden" rotation ...   
But those effects do exist in the real, natural scenario.
By the way, this very morning I saw a clip on Discovery Max tv, where a CD was made rotate at the r.p.m. of a hoover ... The CD suddenly breaks into hundred of small pieces, obviously due to huge tensile internal stresses due to both centripetal and centrifugal forces (the former causing the rotation, and the later the way inertia manifests itself, because all CD particles are being hugely accelerated).
And that, happening in nature, has nothing to do with frames of reference !!