Talk:Centripetal force

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The result of the changing acceleration is surely the centrifugal force for which an equal and opposite centripetal force is required to constrain the circular motion. Rjstott

That's nonsense. Centrifugal force is an imaginary force that appears if you are in a rotating frame of reference. Centripetal force is the force that causes a motion to be circular, producing an acceleration that correspond to a change in the direction of the velocity. --AN

There's nothing imaginary about two opposing forces being equal and opposite. I agree that one is a result of the mass acceleration equation.Rjstott

There is no "equal and opposite force required to constrain the circular motion".

The force equation is F=m a,

In the case of circular motion a=-v^2/r^2r, and F=-m v^2/r^2r. F points inside, and its nature depends on the problem, in the case of a satellite, F = G m M/R^2. Where is the "centrifugal force" in the equations?

There is also the reaction to F, but that acts on another body that depends on the problem, in the case of the satellite, is the force exerted on the earth by the satellite, is that a "centrifugal force". I don't think so. I think you have to reexamine your first year college physics textbooks. --AN

It would be useful if you dated your comments, it's much easier to follow the dates that way, rather than checking the history. I agree with Rjstott for the purpose of Wikipedia. AN, whoever you are, you are surely a person whith a scientific background. You certainly don't need this article in Wikipedia to explain the centripetal force. I wrote the following paragraph in the article:
It is important to understand right from the start that there is no 'default', 'natural' centripetal force. By default, objects tend to move in a straight line, as Newtonian mechanics teaches, away from the 'orbit', so in this context, by default there is only a centrifugal force at work. The centripetal force is being applied either by accident (meteors orbiting a planet) or artificially (satellites orbiting Earth, the object at the end of a rope etc). Therefore, the centrifugal force is a natural component of a circular movement, while the centripetal force is what we conventionally call the force keeping the object 'in orbit'.
That paragraph has since been removed in favor of a more scientific approach. While I can agree that the statements in my explanation might have been misleading or imprecise from a scientific perspective (which is why I didn't revert the subsequent changes), I think they are a lot easier to understand by the person who needs to be explained how the centripetal/centrifugal forces work intuitively. Again, I will not fight for that paragraph, but I would like to see something easier to understand for the casual reader in the introduction.
Let me explain what I mean with my "intuitiveness" concern by using the following example: When a kid spins a rock at the end of rope he intuitively feels the centrifugal force. You will say that's not correct, he is applying the centripetal force, that's what he feels. But by that standard it would be difficult to explain gravity -- following the same rationale, when you lift a suitcase you apply "antigravity" to it. However, the kid will intuitively feel that he's "beating" some force; when you explain that the downward force is called gravity and it's real, he's ready to accept that, although he's applying an upward force himself. People intuitively feel the force they need to "beat" as the real force; the force they apply feels like the artificial part of the equation: the upward force to beat gravity is artificial, the gravity keeping the suitcase on the ground is natural. If you explain things the other way around, you confuse the casual reader. The same applies at an intuitive level with centripetal/centrifugal forces IMHO: if you start the article with an introductory statement which says that the centrifugal force doesn't really exist, that confuses the reader ("then what's the force that I'm beating by holding on to the rope? Maybe I didn't get it right...") and s/he's most probably going to miss the point of the whole thing long before you get to formulas. --Gutza 21:57, 14 May 2004 (UTC)
Cleon Teunissen 20:26, 14 Jan 2005 (UTC) I agree with this. To the casual reader, the newtonian description feels wrong. But if you accomodate the casual reader's pre-newtonian conceptions, you may be accused of misunderstanding the physics. It seems to me that the aim of the article should be to educate the casual reader. Misconceptions need to be adressed.


Mi previous comment is undated because, as you can see in the history, it predates the new software with its fancy automatic dating :) The centrifugal force appears when you consider a rotating frame of reference, so, if you want to add a centrifugal force, you can do it talking about that frame of reference. In a non-inertial frame of reference, as the one that follows a stone tied to a rope, there is a centrifugal force, which must me contrarested by the the tension in the rope, the centripetal force..something like that, that still includes the idea of centrifugal force, but is (i think, but I'm not 100% sure) physically more correct. --AstroNomer 21:59, May 16, 2004 (UTC)

"In the case of an orbiting satellite the centripetal force is gravity" - I'm really not sure about calling gravity a force - isn't it a field? The satellite's weight provides the centripetal force, I did change this once but my change has been reversed. Opinions? Drw25 15:44, 17 Oct 2004 (UTC)

Yes, and weight is mass*gravity. Gravity is a force that acts on anything with a mass. The satellite included. 134.153.18.39 17:28, 28 Oct 2004 (UTC)

Contents

[edit] If it's present in one frame it's present in all frames

In the article it is stated:

In a corotating reference frame, a particle in circular motion has zero velocity. In this case, the centripetal force appears to be exactly cancelled by a pseudo-force, the centrifugal force. Centripetal forces are true forces, appearing in inertial reference frames; centrifugal forces appear only in rotating frames.

That doesn't make sense.
Whenever the velocity of an object is changed by exerting a force, inertia manifests itself. When you hit the brakes of a car, the grip of the tires on the road is necessary for decellerating the car. If an electric car designed to regain energy on decelleration is switched to braking, the manifestation of inertia drives the generators, recharging the car's battery system. Manifestation of inertia can be very powerful, but manifestation of inertia cannot prevent change of velocity, because the power of inertia only manifests itself when there is actual change of velocity.

The same story in the case of centripetal acceleration. There is manifestation of inertia in the centrifugal direction, but this manifestation of inertia cannot prevent the centripetal force from maintaining the circular motion, because the power of inertia only manifests itself when there is actual change of velocity.

The centrifugal manifestation of inertia is present in both the inertial frame and the rotating frame. Going from one frame to another people may ignore it in one frame and acknowledge it in another. Of course, in all frames the same physics is going on, reference frames are mental constructs, changing your perspective from one frame to another is just that: a change of perspective.

Kinematic inertia is like a current circuit with a self-inducting coil in it. This circuit does not offer resistence to current strength in itself, but it does resist change of current strength. The self-induction can/will only jump into action if there is actual change of current strength. --Cleon Teunissen | Talk 23:40, 13 Mar 2005 (UTC)

You would be right considering a frame of any constant velocity. But a rotating frame is constantly accelerating, so it inertia seems to be a force. On a coordinate plane, imagine a dot at (1,1). From a rotating frame, the dot would seem to be undergoing a constant acceleration (force). But really the dot's just sitting there, forces in balance. Same thing with centrifugal force. It is really just the inertia of an object, constantly being pulled against by the centripital force. But from a rotational frame (matching the object's rotation), the acceleration of the object matches the rotation of the plane, and is invisible. Because no acceleration is visible, inertia seems to be a force. This rotational frame stuff is confusing as hell, though, and should really just be a small note in the whole artical.Themissinglint 11:52, 25 August 2005 (UTC)
Yeah, it's confusing as hell, and it took me a long time and help from others to figure it out. I've got it figured out now both in the philosophy of newtonian dynamic and in the philosophy of relativistic dynamics. Almost always it is sufficient to discuss just the newtonian approach, so that is what I almost always do.
The newtonian view is that the only frames you can formulate the laws of motion for are inertial frames. Of course it is straighforward to perform a transformation to a rotating coordinate system and perform calculations in the context of that rotating coordinate system. According to the newtonian view those calculation procedures are mathematical devices to speed up calculations, but not physics. According to the newtonian view the only calculations that have a one-on-one correspondence to reality are calculations in the context of an inertial frame of reference.
Let's say I stand on a small rotating platform, with a vertical pole along the axis of rotation. The platform is rotating, and I hold on the the pole in order to stay on the platform, and because of that the pole bends a little. The pole is exerting a centripetal force on me, maintaining my circular motion. I am exerting a force in centrifugal direction on the pole, bending it a little. The reason I am in circular motion and the pole isn't is that I am not attached to anything else so there is nothing to keep me from being pulled in circular motion. The pole, on the other hand, is securely attached to the platform, and the platform is well fixed to the ground.
The amount of force that the pole exerts on me, and the amount of force that I exert on the pole are the same (Newtons third law). The effect of the forces being exerted is different because I am not attached to anything else and the pole is.
That scenario can be transformed to any rotating coordinate system, the forces that are at play remain the same, (the amount of bending of the pole doesn't change in going to a rotating coordinate system!), only the way the forces are represented may change in the transformation.
Inertia is of fundamental importance, but it's not a force. Newtons third law provides a sieve to decide what is a force and what isn't. Electrostatic attraction/repulsion is a force because it always occurs as a reciprocal pair: charge A exerts a force on charge B, and charge B exerts the same force on charge A. Because it is always reciprocal, there is conservation of momentum in dynamic interactions. Likewise, gravity is a force, as can be seen from for example the technique of gravitational slingshots. It would be very awkward to categorize inertia as a force because inertia doesn't involve two objects exerting a force on each other; inertia involves just a single object.
The above discussion is beyond the scope of the centripetal force article of course, but that is the general background. --Cleon Teunissen | Talk 09:11, 26 August 2005 (UTC)

[edit] Always a real force?

The article claims that centripetal force is always a real force (as opposed to a fictitious force). However, consider an object at rest in an intertial frame and now look at this object from a frame that rotates around another point in the inertial one. As seen from the rotating frame, the object moves in a circle; if we want to do calculations in the rotating frame we need to identify the centripetal force that makes it appear to move in a circle. In this case the centripetal force is as fictitious as the apparent circular motion is; it is provided by the sum of the centrifugal and Coriolis forces. If only I knew how to explain that in the article without excessively confusing the average reader... Henning Makholm 16:20, 24 December 2005 (UTC)

[edit] Units

This comment was inserted in the article by User:67.71.37.250:

      • Anyone know what units? F in newtons? mass in Kg? angular velocity in radians/second?

I default of explicit conversion factors or comments to the contrary, one is supposed to use a coherent system of units (such as SI units, though that is not the only possible choice), and measure angles in radians. I don't think, personally, that it is worth the clutter to repeat this standard convention in every article that includes a formula. (Exceptions may be where one uses relativistic or natural units with c and/or \hbar set to unity. And perhaps in electrodynamics, where there are several different concepts of a coherent unit systsm). Henning Makholm 22:31, 1 January 2006 (UTC)

[edit] Comment

I've heard it said that in modern physics there is no centripetal force associated with gravity because it is not a force, it's a warping of spacetime in response to mass.

In modern physics the warping of spacetime is seen as the mediator of gravitational interaction. Modern physics recognizes four fundamental interactions of nature: Gravitational interaction, electromagnetic interaction, strong nuclear interaction, weak nuclear interaction.
In everyday life we tend to think of forces as touchy/feely concepts, but in physics it is very much abstract. For example in quantum physics electromagnetic interaction is seen als mediated by what is referred to as 'virtual photons'. That does not mean it's actually 'not a force'. Electromagnetic interaction is an interaction between two objects in which momentum is transferred, so it's a force allright. --Cleonis | Talk 10:02, 4 February 2006 (UTC)

[edit] The expressions 'centripetal force' and 'central force'

In the article it is stated:
Centripetal force must not be confused with central force either.

It is my understanding that Newton introduced the concept of centripetal force to give an account of the orbits of the planets and moons and comets of the solar system.

The article seems to state that the concept of centripetal force ought to be confined to perfectly circular motion, which does not occur in real life; every planets orbits the sun in a more or less eccentric orbit.

What kind of meanings of 'centripetal force' are in circulation? Is it general practice to associate 'centripetal force' exclusively with perfect circular motion? Or is it also general practice to have 'centripetal force' and 'central force' completely overlap in meaning?

It seems to me that 'centripetal' only says something about the direction of the force, not whether it is inducing circular motion, or inducing a highly eccentric orbit, as in the case of Halley's Comet.

The whole point of newtonian dynamcis is that to explain the angular acceleration of Halley's comet as it is being drawn closer to the center of the solar system two concepts suffice: the centripetal force of gravity from the Sun, and inertia. (With the force of gravity codified in Newton's law of gravity, and inertia codified in Newton's three laws of motion.) --Cleonis | Talk 10:20, 4 February 2006 (UTC)


[edit] Reasons for deleting of -\mathbf{r} \cdot \mathbf{F}_{c} = 2 T

Dear Utkarsh, I'm very sorry to have deleted your first edits here on Wikipedia, but please allow me to explain my reasons.

  • First, the derivation was too long. For future reference, you might want to derive it in two steps. The definitions of kinetic energy T and the magnitude of centripetal force Fc give the equation
m v^{2} \equiv 2 T \equiv r F_{c}
from which one may derive the desired result F_{c} = \frac{2T}{r}. One may also use the more general vector equation -\mathbf{r} \cdot \mathbf{F}_{c} = 2 T, since the centripetal force is always directed opposite to the radius vector in circular motion.
  • Second, the derivation had a misconception that might have confused some readers. The kinetic energy is a scalar, i.e., a quantity with no direction, whereas the centripetal force \mathbf{F}_{c} is a vector, which has both magnitude and direction (and specific transformation properties under rotation). Scalars and vectors are different types of mathematical objects and cannot be equated, although the magnitude of a vector (itself a scalar) can be equated with another scalar. Moreover, vectors are written in boldface type, scalars with normal font; hence, the derivation incorrectly wrote the kinetic energy in boldface.
  • Third, there is no physical significance to equating the kinetic energy and the magnitude of the centripetal force, although it might be helpful to some people as a mnemonic. As written, it holds only for perfectly circular motion, although you might enjoy reading about the virial theorem, a related result. Unfortunately, Wikipedia is not a collection of facts and such mnemonics, being infinite in possible number, can't be included unless they're in very common use.

I hope this helps you to understand my reasoning, and also guides you to other interesting ideas and places on Wikipedia, such as the virial theorem. Maybe I'll try to spruce that up for you right now. Hoping that your time here at Wikipedia is a happy and productive one, WillowW 07:51, 9 July 2006 (UTC)

[edit] small change

In the section 'Basic Idea', "becoming larger for higher speed and smaller radius" is wrong since, in the equation directly below it, we see that the accelearation increases (in magnitude) with angular velocity AND radius. So I'm going to delete the word smaller, ok?

Another possible mistake is in the introduction where friction is listed as one of the forces that can cause centripetal acceleration: perhaps friction cannot do this because in purely centripetal acceleration, no work is being done (work = force * distance but r is constant). I'm not changing it though since I'm not sure. Adios

[edit] The expressions 'centripetal force' and 'central force'_2

I repeat a question that I asked a year earlier

In the article it is stated: Centripetal force should not be confused with central force

It is my understanding that Newton introduced the concept of csentripetal force for the purpose of discussing the the mechanics and the law of gravity that account for the orbits of the planets and moons and comets of the solar system.

It appears to me that in this article a definition of 'centripetal force' is submitted that deviates from the original meaning. I think many if not most textbooks use the expression 'centripetal force' in the meaning as introduced by Newton: A force with the property that is is at all points in space directed towards the same spot.

I think the distinction that the article suggest between the expressions 'centripetal force' and 'central force' is not justified. I think that most authors use those two expressions interchangebly.

My intention is to edit the article accordingly. --Cleonis | Talk 01:15, 23 January 2007 (UTC)

Hi Cleonis,
I just now noticed your message here, sorry for not replying earlier. It's probably a language thing, but I assure you that the terms "centripetal force" and "central force" are not interchangeable. As I'm sure you know, a central force is defined by its global spatial isotropy, i.e., by its functional dependence only on the distance between the two bodies F(r). By contrast, the centripetal force F = mω2R is not even a force, but a force requirement; the force required to move in a circle of radius R with angular velocity ω. The centripetal force may be supplied by a non-central force, such as the magnetic force or a globally anisotropic force that happens to be isotropic in the plane of the circle at that particular radius R.
Hoping that this clarifies the difference, Willow 12:25, 3 February 2007 (UTC)
I just did a google search with the following words: '"centripetal force"' 'planet' 'sun' 'ellipse'. The pattern that I see is the pattern that I expected to see: educators explain that the planets follow keplerian orbits and that the planets are in orbital motion due to the centripetal force from the Sun. From the way that the expression is used it is clear that the educator intends to convey the understanding that a centripetal force sustains an orbit. (In the case of keplerian orbits: an inverse-square force.)
(There's a historical detail that I think is interesting. When Newton did his computations, he used the following method to find the curvature of a keplerian orbit at each point of its orbit. For each point, Newton constructed a circle, tangent to the keplerian orbit, with a curvature that matched the ellipse's curvature at that point. That gave Newton a handle on the acceleration in the direction perpendicular to the instantaneous velocity.)
My question is: is it necessary to assert that the expression 'centripetal force' is to be used exclusively in conjunction with perfectly circular motion?
I think the following statement would be very odd: "gravity is a centripetal force when it sustains a circular orbit, but when the object's orbit is keplerian instead of circular, then gravity is not a centripetal force." I prefer simple and straightforward: gravity is a centripetal force, regardless of the shape of the orbit that is sustained.
I understand the kind of distinction between the proposed definitions of 'centripetal force' and 'central force', what I doubt is whether it is a wide-spread custom to use that kind of distinction. This wikipedia article is the first time I have encountered this rather technical distinction. --Cleonis | Talk 18:22, 3 February 2007 (UTC)
I have to get back to work, but here's the scoop, according to my understanding. One can divide the force applied to a particle into two components, that which is parallel to its path (and increases its speed) and that which is perpendicular to its path, thereby deflecting it. In some usages, this latter force can be called the "instantaneous centripetal force" and is equivalent to Newton's construction that you cite. However, this usage is somewhat advanced; for first-year college physics students and as an unqualified noun, centripetal force is applied only to circular orbits, as described above. That said, I'm not surprised that one can find mis-understandings and even inaccuracies (e.g., that the centripetal force is itself a physical force) on the web. I do not think that you will find even one mechanics textbook written for physics majors that says anything different from what I have written here; indeed, I encourage you to consult Goldstein or Arnold or Landau or any of the other classic textbooks in mechanics to verify the definitions. Hoping that you trust me, Willow 18:50, 3 February 2007 (UTC)

[edit] Heading

I changed the heading of the first section (after the intro) from "Basic idea," which seemed overly informal to "Quantitative physical description," which I felt accurately characterized the content in the section. The heading was then changed by another editor to "Basic formula." I don't really get the logic behind this choice of heading. In what way is the formula basic? Rracecarr 03:38, 3 February 2007 (UTC)

Hi Rracecarr, here was my reasoning which I summarized too briefly in the edit summary. Centripetal force is a very basic concept in physics, and it's very likely that we'll have young students (say, bright 12-year-olds) and many non-scientists. The section in question explains why centripetal force is needed, what happens if it's too small or too large, and gives its formula without derivation.
WP articles are supposed to be written as simply and accessibly as possible for their intended audience, meaning that we should prefer more simply-worded (but accurate!) formulations over more technical ones. I hope that you'll understand, but the heading "Quantitative physical description" seemed unnecessarily technical to me, and could even be daunting to non-scientists; it does not evoke a clear direct idea of the section's content. I appreciate, though, that "Basic idea" is too colloquial and likewise undescriptive, albeit simpler. The heading "Basic formula" was intended as a compromise with your title, the "formula" capturing the idea of "quantitative", but I see your point. It begs the question: if that's the basic formula, what's the complex formula?
How about this heading: "Basic concept and formula"? That would be longer, but more descriptive than any of our headings so far. I'm open to other ideas as well. Willow 12:11, 3 February 2007 (UTC)

[edit] Elliptical Paths?

The article has:

"The centripetal force is the external force required to make a body follow a circular path at constant speed. The force is directed inward, toward the center of the circle."


Issues:

  • What about an elliptical path?
  • An elliptical orbit is not at constant speed
  • Is the centripetal force in an elliptical orbit directed toward both foci of the ellipsis or only one focus (assuming an orbit around only one object)?
  • Isn't the force actually directed toward the center of mass of the two objects not the center (or focus/foci) anyway?

[edit] Clarification of Solid Object Example

This is what I think the solid object example should be expanded to say:

" For a solid spinning object, tensile stress is the centripetal force that holds the object together in one piece. The force acts perpendicularly to the axis of rotation, in a complex network of lines of force determined by the molecular structure of the material. "

With a final sentence of whichever is correct:

" The force acts toward the center of mass between the axis of rotation and the outer edge of the object, along each line of force. "

Or...

" Each line of force stretches from one side of the object to the other side, transecting the axis of rotation, and the force acts towards the center of mass of each line of force. "

I would put this solid object example in a separate paragraph after the gravity and string examples.

[edit] Diagram is wrong?

Image:Centripetal_derivation_circles.png

Is it just me, or is the second circle in this diagram incorrect? The velocity vectors, as shown on the left, are tangent to the circle, not pointing outwards as on the right. The acceleration vectors should point inwards, not tangent to the circle. An object traveling around the circle on the right would not have velocities or accelerations at the

Am I misunderstanding the diagram? (The text of the article where it refers to the diagram is OK, but the diagram itself seems excessively confusing.)

--BlckKnght 00:52, 16 March 2007 (UTC)

Well, I've just re-read the article more carefully and now I understand why the diagram is drawn the way it is. I am concerned though that because this is the only diagram in the article it may cause confusion about exactly which direction the velocity and acceleration vectors point as an object moves around a circular path. Could another diagram be made that is like the circle on the left of this one, but with an additional inward pointing acceleration vector? If we put that one higher up the page I think it would improve things. If I have time, I'll try to make one myself.

--BlckKnght 03:17, 16 March 2007 (UTC)

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