Talk:Centripetal force/Archive 1

Roller coaster error
The text beneath the image of the roller coaster could be argued to suggest that roller coasters are held onto their tracks by centripetal force alone. —Preceding unsigned comment added by 67.183.23.68 (talk) 17:27, 23 July 2010 (UTC)

Forgetting the basics?
The article doesn't even mention the basic Fc = m*v^2/r formula, isn't that usually the first one that is encountered in High School physics books? —Preceding unsigned comment added by 209.195.102.103 (talk) 19:48, 10 June 2009 (UTC)


 * Indeed, that does seem silly. I just added that formula, as well as the other common one using angular velocity; with sources even, so that they are verifiable and the assumptions underlying them can be checked.  Dicklyon (talk) 05:57, 23 June 2009 (UTC)

Changing acceleration
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 with 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.


 * I disagree with those of you who believe making reference to a "centrifugal force" will be useful for novices (especially students) who come to this page looking for an explanation of centripetal force. I currently rely on a first year college physics textbook to do my first year college physics homework, and that text warns against the idea of a centrifugal force. In fact, since my first physics course in high school, I have been told that there is NO centrifugal force; that in an inertial reference frame an object remains in circular motion instead of continuing to travel in the direction of its tangential velocity because of the pull of some centripetal force.  Mentioning a centrifugal force that does not exist because it is more "intuitive" is a disservice to those who want to learn about the physical reality of the centripetal force, which, after all, is the topic of this article.  It is a disservice to anyone beginning to study Newtonian physics, whose predictions are often counter-intuitive. I like the content of the common misunderstandings section, and I believe "centrifugal force" should be discussed there. By stating its existence in the introduction the authors have given validity to a concept that every physics teacher I have ever had (and every physics textbook) has expressly cautioned us not to use.  Please delete the reference to centrifugal force in the introduction, and if there is some valid time, place, reference frame, etc. to consider centrifugal force, make sure this is clear in the common misconceptions section and in the centrifugal force article.  - MIT Freshman, 21 Feb. 2008  —Preceding unsigned comment added by 18.202.1.85 (talk) 03:53, 22 February 2008 (UTC)

My 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)

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)

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)

For the (more) average reader: No frame of reference can be considered to be the "correct" or "real" frame of reference, all frames of reference can only be described relative to each other. Hence, if a force appears from a rotating reference frame (ie centrifugal force), then it is every bit as "real" as a force that appears from an internal reference frame (ie centripetal force) —Preceding unsigned comment added by 84.71.66.130 (talk) 08:57, 3 April 2008 (UTC)

Units
This comment was inserted in the article by User:67.71.37.250: 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)
 * Anyone know what units? F in newtons? mass in Kg? angular velocity in radians/second?

I believe an example using units would be helpful for someone learning the concept. However, I agree with Henning that it may add clutter to discuss units for every equation presented but perhaps a compromise is to include units in the 'example’ section...(March 26, 2008) —Preceding unsigned comment added by 71.232.14.193 (talk) 20:35, 26 March 2008 (UTC)

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)

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)

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 $$F_{c}$$ 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)

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

If we keep the speed constant but decrease the radius of the path then the centripetal force must increase to bring this about. Similarly if we keep the radius the same but decrease the radius then the centripetal force must also increase. I sounds like you (unsigned poster above) are confusing speed with angular velocity. Certainly increasing radius while keeping angular velocity the same will increase the centripetal force. But to increase the radius while keeping angular velocity the same you must increase the speed since the angular velocity is related to speed and radius by omega = v/r.

Friction can most certainly cause centripetal acceleration. This is what keeps your car on the road as you go around a corner. Perhaps it is easier to think of the example of an object on a turntable. If the turntable were perfectly smooth (frictionless) the object would slide off because of its tendency to move in a straight line in the absence of forces. If the turntable is not perfectly smooth then the object can stay on precisely because the friction due to the surface of the turn table provides the necessary force (centripetal) to curve the object's path into a circle. (GLeeDads (talk) 04:15, 6 February 2009 (UTC))

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)

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)

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: —Preceding unsigned comment added by 75.7.44.72 (talk • contribs)
 * 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?

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. —Preceding unsigned comment added by 75.7.20.57 (talk • contribs)

Bold text== Diagram is wrong? ==



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)

71.251.176.164 (talk) 16:34, 5 May 2008 (UTC)==Centripetal force does not exist???== Well, as someone who took more physics courses than I can count (I've lost track: 8? 9?), I was rather surprised to see this:  "Furthermore, the name suggests a fundamental force, which it isn't. The latter causes great confusion with students who erroneously add the force to free body diagrams. As such, engineering texts, in particular, have disposed of its use."

Hmmm. Interesting. I'd like someone to explain, if centripetal force does not exist, what keeps a ball on a string? If no force exists, then the ball should just fly off into space, following its inertia. - Theaveng (talk) 13:02, 10 December 2007 (UTC)


 * I would support removing that paragraph from the lead; it sounds more like opinion than encyclopedic content. It is true that "centripetal force" is not a fundamental force (in the sense that "centripetal" does not name a cause for a force to exist, such as e.g. Lorentz force does), but it is only possible to extract that meaning from the paragraph if one already knows that which it is supposed to tell. In fact, the paragraph would make no more nor less sense if transplanted verbatim to centrifugal force, which strongly suggests that it adds very little meaning to the article. –Henning Makholm 22:37, 22 December 2007 (UTC)


 * On further thought, I went ahead and deleted it. –Henning Makholm 01:18, 23 December 2007 (UTC)

Question regarding your definition. Since you state that the centripetal force acts towards the center of mass, in the case of two equal mass stars in mutual orbit, the centripetal force suddenly changes direction at the center of mass between the two stars. When what was an attractive force from one star becomes a repulsive force beyond this point. And conversely, the same occurs for the other star but with forces in the opposite direction. What causes this sudden change in the direction of the centripetal force that implies that the force ceases to exist at the center of mass???71.251.176.164 (talk) 16:34, 5 May 2008 (UTC)


 * The centripetal force in this case is gravity. At the center of mass, the gravitational forces are equal and opposite and add to zero. -- SCZenz (talk) 16:27, 11 May 2008 (UTC)


 * 71.251.176.164, the centripetal force in a gravity orbit is always gravity, and no forces in a gravity orbit ever reverse directions within the context of polar coordinates. You need to study the differential equation for a planetary orbit and examine the general picture.


 * You were quite wrong to put in the conversion between polar and Cartesian coordinates and claim it to be a derivation of centripetal force. No centripetal force is stated in that derivation. Centripetal force could come from the tension in a string or a spring, or from gravity, or from electrostatics, or from F = qvXB, or from the normal reaction of the floor of a rotating spacecraft. But there is no centripetal force implied in that derivation.David Tombe (talk) 04:33, 12 May 2008 (UTC)

The so-called derivation in polar coordinates
The derivation in the main article acually applies to Coriolis acceleration, centrifugal acceleration, and Euler angular acceleration. It is merely a conversion between Cartesian and polar coordinates and it doesn't imply any kind of motion in particular. It is most certainly not a derivation of centripetal force.

It should either be removed completely or transferred to the centrifugal force and Coriolis force pages.David Tombe (talk) 08:32, 11 May 2008 (UTC)


 * David: I don't agree with you at all about this. The derivation is an application of kinematics and determines the forces that must be applied to achieve a specified path r ( t ). All that is done is to find d2r / dt2, the acceleration, in an inertial frame of reference. The final example of this section for circular motion shows in particular the usual result for centripetal force, directed radially inward. A complete published discussion is . Brews ohare (talk) 14:20, 11 May 2008 (UTC)

Brews, the proof comes when we apply these equations to planetary orbital theory. The centripetal force is the gravity force. The term which you think is the centripetal force acts in the opposite direction to gravity.

I am in absolutely no doubt about this. I did orbital mechanics in depth. Those expressions that you have derived above are the inertial forces, ie. centrifugal, Coriolis, and Euler.

In the special case of circular motion, the centrifugal force and the centripetal force will be balanced. Hence, if you do the vector diagram for the velocity tangents, as you did above, you will indeed get an expression for the inward acting centripetal force in the same form as the centrifugal force.

When the two are not balanced, we get an ellipse, parabola, or hyperbola. David Tombe (talk) 04:24, 12 May 2008 (UTC)


 * Brews, one more important point. Any directions that are implied by the derivation in question are merely a consequence of vector notation. No actual physical situation is implied. Directions only become sorted out correctly once we model a real physical situation. When we model the gravity orbit, the sign on the expression that you thought referred to centripetal force becomes opposite to that of the inward acting gravity force. It is the gravity force that is the centripetal force. I think that you were assuming that because the derivation put a negative sign against the term in question, that you thought that this means that it must be centripetal force. David Tombe (talk) 04:39, 12 May 2008 (UTC)
 * Well, I see a lot of chatter, but no substance here. The math is clear and the results agree with at least three cited references, some of huge reputation, the others in texts that are less famous but still used as university texts. You yourself agree that the formulas are correct, and argue over "limitations" which you simply pontificate about, without support of any consequence, neither citations nor focussed criticism of the mathematical details. So the formulas are OK, the results and the way they are used have been corroborated by numerous citations, and a lot of rhetoric is not going to go anywhere. Brews ohare (talk) 12:54, 22 May 2008 (UTC)

Revisions
I have rewritten large sections of the introductory paragraphs to consolidate discussion of uniform motion, to avoid repetition, to make the flow more logical (at least to me), and to clarify the kinematic aspect of this article. I hope the revision is successful. Brews ohare (talk) 17:55, 15 May 2008 (UTC)

Local coordinates and curvature
The present discussion of local coordinates, while accurate and well documented, lacks a reference or discussion about the neglect of the variation of the radius ρ between location s and location s + ds. For example, the arc length and θ satisfy ds = ρ dθ, not, for example, ds = 0.5 [ρ(s) + ρ(s+ds)] dθ. It appears from the construction of the osculating circle, because it is a three-point construction, that the osculating circle is an accurate method to find acceleration and implicitly avoids any such issue with ρ, because acceleration also is a three-point determination. (In a finite difference viewpoint it is a second difference.) However, I have not found an explicit description of this point. Perhaps someone more versed can help? Brews ohare (talk) 15:50, 30 June 2008 (UTC) I've added a section "Alternative Method" that avoids the issue, but a frontal attack would be interesting. Brews ohare (talk) 03:43, 2 July 2008 (UTC)

Yo-yo example
I cannot see any connection in this example to centripetal force. It looks to me like a conversion of rotational kinetic energy to gravitational potential energy and back again. Please explain in more detail. You might also consider adding some references: Nonsmooth Mechanics Classical Mechanics Predicting Motion. Brews ohare (talk) 20:56, 19 January 2009 (UTC)

I've taken a stab at rewriting this example. Brews ohare (talk) 23:02, 19 January 2009 (UTC)


 * Brews, What you do is, you ignore the gravity and you ignore the roll. A yo-yo works just as well when no gravity is involved.


 * Simply look at the translational motion of the centre of mass of the yo-yo. It moves down one side, does a U-turn, and then moves up the other side. The centripetal force causes the U-turn. The centripetal force is in turn caused by the tension in the string when the string is fully unwound. That tension is transmitted directly through the centre of mass of the yo-yo. David Tombe (talk) 04:52, 20 January 2009 (UTC)

Brews, I've just looked at your amendment. It seems that you now understand it fully. That was a relatively easy one as far as identifying the reversal force was concerned. Have you ever managed to identify the source of the reversal torque in the rattleback?

I have attributed the rattleback reversal torque to 'real' Coriolis force. A couple of days ago, it came to my attention that in a peer reviewed paper that came out in 2008, two professors have linked the reversal torque to Coriolis force as per the textbooks. I'm fascinated to see how textbook Coriolis force can produce a real effect. I'm hoping to read that paper maybe today. David Tombe (talk) 04:59, 20 January 2009 (UTC)

Definition?
Is there a generally accepted definition of centripetal force? It looks to me like there are two, not often clearly distinguished. In one, it's the force orthogonal to direction of motion, directed toward the center of the osculating circle. In the other, it can be any force, such as the gravitational force even when the orbit is not circular. Do we need to discuss the exitence of both, and clarify the relationship? Dicklyon (talk) 14:09, 5 June 2009 (UTC)


 * I have added a source to the already provided source suggesting that centripetal force always is the force directed toward the instantaneous center of curvature. This point is made clear as well in the analysis of the section Centripetal_force. One way to look at it is that any definition of centripetal force must reduce to the case of uniform circular motion in the appropriate limit.


 * If you have a source suggesting a looser definition, I'd suggest that it is simply a misuse or a non-technical use of the term "centripetal force". The word "centripetal" after all is used in ordinary English in a broad sense, but that usage is not appropriate in this technical article. Here is a cute example of non-technical usage. Brews ohare (talk) 16:23, 6 June 2009 (UTC)


 * Well, probably you're right, but there are quite a few books (like this) that seem to mention centripetal force with respect to gravity, without restricting to a circular orbit. Sort of like David's lead that I reverted where he said it was the force in a central-force problem.  So if you're right, then the reciprocal r-square gravity term in David's favorite equation, the gravity force, is not exactly a centripetal force, except when the orbit is circular (or at apogee or perigee).  I just want to make sure we don't let such loose language creep in if it's not supported by good sources. Dicklyon (talk) 00:53, 9 June 2009 (UTC)

I've attempted to beef this up in the introductory paragraph. Unfortunately, Newton himself doesn't have a really precise and concise (or even unique) definition. ET Whittaker avoids the use of the word "centripetal" entirely. Brews ohare (talk) 18:47, 9 June 2009 (UTC)

Sources and other work needed
This article has grown to about 50 KB with a bunch of long unsourced symbol-soup derivation sections. This is not an appropriate encyclopedic style, in my opinion. Do you agree? I think we should shorten these, leave out a lot of steps, given an outline of the idea, and results in simpler notation more like what's in Taylor for example. It's not clear that the article's "inflatinary phase" of May/June 2008 was a net improvement, and it's time to review that and see what we can do to fix it. Anyone want to help? Dicklyon (talk) 16:04, 21 June 2009 (UTC)

I added a basic formula section, with sources, and added sources and more info to the short section on Sources of centripetal force. The rest of the article, the Analysis of several cases, is almost entirely unsourced, and should be either fixed or removed. It's a bit too complex to keep as is, or for me to work on incrementally without knowing what sources it is following. Dicklyon (talk) 06:07, 23 June 2009 (UTC)

Symbol-soup
This is a catchy phrase. I take it to mean a mathematical derivation should rarely appear in Wikipedia, and the article should contain "just the facts, Mam", as Sargent Friday says.

However, detailed derivations are useful, set up the notation, and provide the context of the result (e.g. the approximations used). They help the mathematically less sophisticated to get the drift. They provide logical authority to shore up Wikipedia's major shortcoming: lack of vetted authorship.

Once accustomed to the language, one realizes that a mathematical derivation is a bit more than mechanical shifting of equivalent symbolic expressions back and forth. The formalism is a succinct expression of ideas. with built-in safeguards against the tendency to shift meanings around, which does occur in verbal descriptions.

Also, teen-agers are not the entire Wikipedia audience as is very evident on looking at the articles present; they include, for example, completely unintelligible (to me) articles on differential geometry.

I see no reason to enforce a limited content in Centripetal force or anywhere else. The article should contain information useful to as broad a spectrum of readers as possible, but that doesn't mean everything said should be intelligible to every reader. Brews ohare (talk) 18:13, 22 June 2009 (UTC)


 * Thanks for noticing how catchy it is. The point of this descriptor is that a symbol soup section has a style that makes it somewhat inappropriate as an encyclopedia article, since what it's trying to tell you is highly encoded in lengthy math, which dominates both the appearance and the content of the section, making it very hard to read, especially for the non-specialist.  I've written enough symbol soup myself to know how easy it is to write when you understand something in that way, but I'm also familiar with how hard it is to read.  Since we're writing an encyclopedia, a main goal is to impart understanding.  Imparting a detailed derivation that can be followed step-by-step is generally not an important goal; sometimes it's OK, but when an article starts to be heavy with such sections, I think something is very wrong, and it should be addressed by simplification of the presentation.  Dicklyon (talk) 22:01, 22 June 2009 (UTC)


 * The book cited for the banked turn presents it in one equation (5.37 on p.128). Why do we need four?  The two derivation sections before it that I tagged as being without sources don't provide a clue as to whether these derivations are conventional, important, or not.  Even a textbook probably wouldn't devote so much symbol soup to something so simple, I suspect.  Let's source them, and then fix them to be no more complex than their sources, OK?  Similarly with the unsourced and undersourced sections that follow. Dicklyon (talk) 22:08, 22 June 2009 (UTC)

Well, it is a judgment call. I am inclined to lean farther toward equations than you are. That is something I learned from Wikipedia, where all kinds of verbal arguments could be boiled down to either agree or disagree with the math. Two such experiences occur regularly on Centrifugal force, where D Tombe has his version and the "curvilinear coordinate" Centrifugal force people have theirs. Maybe the reader could do without this math, but without the math the article simply oscillates forever as one mess of verbiage and assertion is replaced by the opposite and so on and so on. Brews ohare (talk) 23:55, 22 June 2009 (UTC)

Besides the influence of math upon the dynamics of Wiki articles, I do find for myself that I do not believe a Wiki article that simply cites a result and a source. I have found sources so misrepresented, and sometimes totally unavailable that a math derivation is much more persuasive. This lack of credibility is a major problem of Wikipedia, and at least in technical areas can be overcome by leaning more toward detailed argument than a regular print encyclopedia where such argument is limited by space, and is somewhat less necessary because the author is vetted. Brews ohare (talk) 00:00, 23 June 2009 (UTC)


 * I think you're expressing a variant interpretation of WP:V. I prefer a more conventional interpretation.  Dicklyon (talk) 04:37, 23 June 2009 (UTC)

I believe there is a school of thought that wishes to avoid making a Wiki article in to a Wiki book. However, short of becoming a book, but leaning toward greater detail than a print encyclopaedia, instructional aspects can have a larger role in Wikipedia than in a print encyclopaedia because space is less an issue. Also, debate over how this instructional material should be presented will lead to better presentation in the long run, I hope. And finally, as things stand at the moment (just between myself and the wall) the Wikibooks are in a dreadful state, and often are totally crackers. I think that happens because a book is too large an undertaking for the interactive, sound-bite type of development, and so are more likely to be a one-author enterprise proselytizing some odd ideas. Brews ohare (talk) 00:07, 23 June 2009 (UTC)


 * I think that wikibooks is a mess because a wiki isn't a good way to write a book; let's stick to writing an encyclopedia. Dicklyon (talk) 04:37, 23 June 2009 (UTC)

Better simple definition?
Unless I'm missing something in this, it seems like a good "entry-level" definition for centripetal and centrifugal forces would be something like:

"A pseudo-force is an imaginary force that is the apparent result of the combination of real forces acting on an object, or the "explanation" for what the object is doing. Centripetal and centrifugal forces are the imaginary forces that "explain" why an object is tending to move in a circular direction.  They are complimentary- if the centripetal force and the centrifugal forces are equal, the object is moving in a circle.  Imagine a ball moving in a circular path, on a string around a fixed point.  It is exerting (pulling) a force of X on the string.  That is the centrifugal force.  At the same time, the string is exerting an equal but opposite (-X) force on the ball.  This is the centripetal force.  If some force acts on the ball that increases its speed, it will pull harder on the string.  As the string stretches, there is more centrifugal force than centripetal force and the ball moves further away from the center point. Once the force stops acting, the system tries to recover. If the string is springy, it will pull back on the ball (increasing the centripetal force) and try to pull it back toward the center. If the string is not springy, the ball will simply speed up and the circular forces on the string will maintain equilibrium. If the string breaks, the both forces disappear- nothing is pulling the ball toward the center, and the ball is no longer pulling away from the center. It simply goes in the straight line its inertia causes it to go.

To use frames of reference, if you are standing on the ball holding the string, you will feel it pulling on you. This is the centripetal force. If you are at the center point holding the string, you will also feel it pulling on you. This is the centrifugal force. It is the same effect, with different names depending on frame of reference.67.167.249.170 (talk) 15:17, 29 July 2010 (UTC)

Clear and Simple derivation of $$ F = \frac{m v^2}{r} $$
The derivation of the commonly cited equation:


 * $$ F = \frac{m v^2}{r} $$

Under Geometric Derivation uses an analogy to justify a major step. I don't see how the stated equation follows although it does give the correct result. I propose the following derivation as a clear and simple alternative that doesn't skip or obscure any of the steps.

Equations for uniform circular motion in terms of an arbitrary time $$b$$ :


 * $$ x = r \cos(b) \quad\quad\quad\quad y = r \sin(b) $$

The circumference of circle is $$ 2 \pi r $$ so given a velocity, $$v$$, one revolution occurs when:


 * $$ b = \frac{2 \pi r}{v} $$

At this point $$ x = r $$ and $$ y = 0 $$ This will be the case if the arguments in the cos and sin equal 1

Applying this constraint:


 * $$ x = r \cos \left( \frac{v b}{2 \pi r} \right) \quad\quad\quad\quad y = r \sin \left ( \frac{v b}{2 \pi r} \right) $$

The units of time and distance are arbitrary so make the following variable substitution:


 * $$ t = \frac{b}{2 \pi} $$

which gives:


 * $$ x = r \cos \left( \frac{v t}{r} \right) \quad\quad\quad\quad y = r \sin \left ( \frac{v t}{r} \right) $$

Take second derivatives with respect to t to get accelerations $$ a_x $$ and $$ a_y $$


 * $$ a_x = \frac{d^2}{dt^2} r \cos \left( \frac{v t}{r} \right) = -r \cos \left( \frac{v t}{r} \right)\frac{v^2}{r^2} \quad\quad\quad\quad a_y = \frac{d^2}{dt^2} r \sin \left( \frac{v t}{r} \right) = -r \sin \left( \frac{v t}{r} \right)\frac{v^2}{r^2} $$

Adding the acceleration vector magnitudes to get total acceleration magnitude:


 * $$ |a|^2 = |a_x|^2 + |a_y|^2

$$
 * $$ |a|^2 = r^2 \cos^2 \left( \frac{v t}{r} \right)\frac{v^4}{r^4} + r^2 \sin^2 \left( \frac{v t}{r} \right)\frac{v^4}{r^4}

$$
 * $$ |a|^2 = r^2 \frac{v^4}{r^4} \left( \sin^2 \left( \frac{v t}{r} \right)+ \cos^2 \left( \frac{v t}{r} \right)\right)

$$
 * $$ |a|^2 = \frac{v^4}{r^2} \left( \sin^2 + \cos^2 \right)

$$
 * $$ |a| = \frac{v^2}{r}

$$
 * $$ |F| = m |a|

$$
 * $$ |F| = m \frac{v^2}{r}

$$

MaxLupton (talk) 18:23, 18 October 2010 (UTC)
 * Hi, I have reverted your edits. Please have a careful look at wp:RS, wp:V and wp:NOR. Cheers - DVdm (talk) 21:06, 18 October 2010 (UTC)

Sources of centripetal force
The section entitled 'sources of centripetal force' has strayed away from the point. All we need to say is that gravity is the source of centripetal force in a Keplerian orbit. We don't need all that extra stuff about centres of mass, which is badly written anyway. We do however need a few more examples of other kinds of centripetal force. We have got a 'pull' example, as per the tension in a rope. We should also add a 'push' example, such as in the case of the normal reaction in a wall of death rider. David Tombe (talk) 22:42, 4 November 2010 (UTC)


 * I think the content you removed was relevant and properly sourced, so I restored it. DVdm (talk) 22:48, 4 November 2010 (UTC)

Well I'm not so sure. The section is entitled sources of centripetal force. So all we need to say for that particular case scenario is that the centripetal force is supplied by gravity. I was in the process of re-wording the bit about Newton considering gravity to actually be a 'centripetal force', but I got interrupted by your message on my talk page. As regards planetary orbits, as you probably know, I was all in favour of having a short section on planetary orbits over on the centrifugal force page. But the particular manner in which the information on planetary orbits is written in this article does not do the topic justice, apart from being irrelevant in the context. We need to take a general approach, using the radial and transverse equations, and explaining how the general solution is a conic section. Circular orbits are only a very special case. Gravity is of course the centripetal force in the context, which is all that matters for the section in question. David Tombe (talk) 22:59, 4 November 2010 (UTC)


 * I think the section is well balanced and doesn't need re-wording, so I propose to keep it. DVdm (talk) 23:05, 4 November 2010 (UTC)

That 'Complete Idiot's Guide to Physics' which you have used as a reference treats planetary orbits in a totally non-analytical fashion, and it seems to have got the transverse forces in non-circular orbits all mixed up with the gravitational force which is always radial. David Tombe (talk) 00:49, 5 November 2010 (UTC)

The Definition of Centripetal Force
The article currently uses a definition of centripetal force as being the force acting normal to a trajectory. Most sources seem to focus exclusively on the special cases of circular motion and therefore this definition wouldn't be an issue. But I was wondering, in the case of a non-circular Keplerian orbit where the gravitational force is directed towards a fixed origin, called 'the focus', whether or not the definition given in this article is correct or not. I would have been inclined to have defined centripetal force as being a force which acts towards the fixed centre of a rotating system. In which case, I would view the centripetal force in a Keplerian orbit as being exactly the gravitational force. However, under the definition given in the article, the origin in a Keplerian orbit will move around and the centripetal force will only be a component of gravity. I am inclined to believe that my view was the general view at least some time in the past. Can anybody clarify this issue? David Tombe (talk) 11:14, 6 November 2010 (UTC)


 * The definition given in the article is properly sourced and is perfectly okay for non circular orbits ("...the instantaneous center of curvature of the path"). If you have a source that defines centripetal force as being a "force which acts towards the fixed centre of a rotating system" then please present it. Otherwise I think this inquiry is off-topic. DVdm (talk) 11:46, 6 November 2010 (UTC)

Dvdm, This enquiry is not off-topic. I have reason to believe that Newton considered gravity to be a centripetal force acting towards the focus of the ellipse. All I want to know is what the official definition of centripetal force is nowadays, and I'm not going to judge that on the basis of one source. I want to know if there is any ambiguity about this, or if the definition has changed since the time of Newton to the one at the beginning of this article? Unfortunately most sources only talk in the special context of circular motion and so that doesn't help any, since the two concepts overlap in that case. David Tombe (talk) 15:07, 6 November 2010 (UTC)


 * The given sources for the definition clearly do not "only talk in the special context of circular motion". If you have a source that warrants the replacement of the currently sourced definition, then you might be on topic. Inquiring "what the official definition of centripetal force is nowadays", and "if the definition has changed since the time of Newton to the one at the beginning of this article" should be done at the reference desk, and are off topic here. Go ahead, try the ref desk. DVdm (talk) 16:41, 6 November 2010 (UTC)

Dvdm, I'm getting a bit confused here. John Blackburne has just stated over on the talk page at centrifugal force that,

Even if it were properly sourced the introduction is not the place to introduce sourced material. John Blackburne

Yet here at centripetal force you are putting alot of emphasis on the importance of sources as regards the initial definition. That issue will need to be ironed out before we can properly address the content issues. David Tombe (talk) 20:01, 6 November 2010 (UTC)


 * Please stop disrupting this article talk page with these off-topic remarks. What X says on the talk page of article Y in context Z, has nothing to do with what U says on the talk page of article V in context W. DVdm (talk) 20:12, 6 November 2010 (UTC)