Talk:Centripetal force/Archive 1

2233:"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. 291:

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

4083:

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?

2109:

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.

2001:) 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. 2192:

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.

504:). 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 1279:

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?

4206: 1185:(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.) 31: 1817:. 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? 3239: 1022:, 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. 1468:==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." 1273:, 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. 266:

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. --

1734:

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.

432:

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.

2947: 4122:

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.

1749:"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. 1070:

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.

4137:

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

2042:

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

1530:

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

1201:

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

1111:

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

465:

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

348:

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

282:

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

4031:

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

2057:

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

431:

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

375:

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:

313:

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

260:

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

4026:

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',

2191:

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 Knowledge (XXG) than in a print encyclopaedia because

2156:

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

2108:

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

1278:

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

1073:

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

1064:

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

643:

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

2141:

Well, it is a judgment call. I am inclined to lean farther toward equations than you are. That is something I learned from Knowledge (XXG), 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,

2084:

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

1733:

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,

1258:

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

1181:

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

688:

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

421:

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

3526: 1974:

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

1899:

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

1748:

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

1443:

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

1427:

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

1242:

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

1069:

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

411:

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

397:

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

290:

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

4121:

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

1712:

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

1609:

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

521:

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

3995:

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

2236:

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

2125:

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

1925:

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

231:

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

200:

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.

1141:

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

2080:

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 Knowledge (XXG)'s major shortcoming: lack of vetted

1211:

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.

4082:

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

2142:

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.

1945:

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

1237:

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,

379:

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.

239:

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

355:

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

1444:

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.

1574:

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

1074:

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. (

572:

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

1531:

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???

3686: 3234:{\displaystyle a_{x}={\frac {d^{2}}{dt^{2}}}r\cos \left({\frac {vt}{r}}\right)=-r\cos \left({\frac {vt}{r}}\right){\frac {v^{2}}{r^{2}}}\quad \quad \quad \quad a_{y}={\frac {d^{2}}{dt^{2}}}r\sin \left({\frac {vt}{r}}\right)=-r\sin \left({\frac {vt}{r}}\right){\frac {v^{2}}{r^{2}}}} 265:

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

2020: 398:

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.

2157:

credibility is a major problem of Knowledge (XXG), 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.

606:

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)

4062:

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.

2363:

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.

677:

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?

1030:, 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 422:

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.

149:

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.

261:

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

1060:

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?

2732: 325:"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? 1773:

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.

1564:

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

637:

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

363:

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

2883: 1848:

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:

2092:

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.

1917:

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

441:

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

1107:

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.

451:

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

392:

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

1649:, 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 1976: 1158:

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

1243:

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,

356:

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

2126:

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.

3784: 3348: 1487:

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

1370:

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. "

2043:

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?

1705:

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.

1182:

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.)

2018:

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"

1496:

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

673:

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.

212:. AN, whoever you are, you are surely a person with a scientific background. You certainly don't need this article in Knowledge (XXG) to explain the centripetal force. I wrote the following paragraph in the article: 122:

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.

2088:

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

3996:

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.

1471:

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. -

4185:

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.

3532: 2461: 1853: 1998: 1850: 1115:

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.

971: 753: 316:

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

3342: 4138:"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. 2620: 873: 2077:

This is a catchy phrase. I take it to mean a mathematical derivation should rarely appear in Knowledge (XXG), and the article should contain "just the facts, Mam", as Sargent Friday says.

4170:

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.

4027:

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

3939: 1652: 466:

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

3835: 1709:

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.

1387:" 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. " 2554: 2358: 2295: 922: 2787: 2776: 1793:

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

4032:

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.

1016: 470:. 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. 633:

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.

1630:

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

3885: 670:

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.

143:

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.

2490: 595: 2940: 2913: 814: 2609: 2583: 1284:

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.

1229:

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

219:

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

2510: 2385: 787: 1856: 3521:{\displaystyle |a|^{2}=r^{2}\cos ^{2}\left({\frac {vt}{r}}\right){\frac {v^{4}}{r^{4}}}+r^{2}\sin ^{2}\left({\frac {vt}{r}}\right){\frac {v^{4}}{r^{4}}}} 74:

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.

1431:

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.)

1422: 1328:

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)?

256:

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

208:

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

197:

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?

100:

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?

2230:

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

3692: 1969:. 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. 1154:). By contrast, the centripetal force F = mωR is not even a force, but a force requirement; the force required to move in a circle of radius 318:..something like that, that still includes the idea of centrifugal force, but is (i think, but I'm not 100% sure) physically more correct. -- 156:

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

107: 1042:

I hope this helps you to understand my reasoning, and also guides you to other interesting ideas and places on Knowledge (XXG), such as the

3681:{\displaystyle |a|^{2}=r^{2}{\frac {v^{4}}{r^{4}}}\left(\sin ^{2}\left({\frac {vt}{r}}\right)+\cos ^{2}\left({\frac {vt}{r}}\right)\right)} 2238: 1546:

The centripetal force in this case is gravity. At the center of mass, the gravitational forces are equal and opposite and add to zero. --

1532: 1457: 1035: 402: 614: 1379:" 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. " 529: 81: 3957: 1050: 1046:. Maybe I'll try to spruce that up for you right now. Hoping that your time here at Knowledge (XXG) is a happy and productive one, 1965:

is the force directed toward the instantaneous center of curvature. This point is made clear as well in the analysis of the section

1946:

gravitational force even when the orbit is not circular. Do we need to discuss the exitence of both, and clarify the relationship?

298: 769:, the derivation was too long. For future reference, you might want to derive it in two steps. The definitions of kinetic energy 685:

of the force, not whether it is inducing circular motion, or inducing a highly eccentric orbit, as in the case of Halley's Comet.

1587:, or from the normal reaction of the floor of a rotating spacecraft. But there is no centripetal force implied in that derivation. 2393: 1407: 1349: 1126: 568:

I default of explicit conversion factors or comments to the contrary, one is supposed to use a coherent system of units (such as

697: 1890:

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.

1661: 2207:

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.

927: 709: 479:

The above discussion is beyond the scope of the centripetal force article of course, but that is the general background. --

247:. Again, I will not fight for that paragraph, but I would like to see something easier to understand for the casual reader 2727:{\displaystyle x=r\cos \left({\frac {vb}{2\pi r}}\right)\quad \quad \quad \quad y=r\sin \left({\frac {vb}{2\pi r}}\right)} 1198:

to assert that the expression 'centripetal force' is to be used exclusively in conjunction with perfectly circular motion?

762:, I'm very sorry to have deleted your first edits here on Knowledge (XXG), but please allow me to explain my reasons. 1331:

Isn't the force actually directed toward the center of mass of the two objects not the center (or focus/foci) anyway?

597:

set to unity. And perhaps in electrodynamics, where there are several different concepts of a coherent unit systsm).

3250: 4213: 38: 823: 484: 385: 332:

Yes, and weight is mass*gravity. Gravity is a force that acts on anything with a mass. The satellite included.

2878:{\displaystyle x=r\cos \left({\frac {vt}{r}}\right)\quad \quad \quad \quad y=r\sin \left({\frac {vt}{r}}\right)} 644:

interaction is an interaction between two objects in which momentum is transferred, so it's a force allright. --

4098:

The definition given in the article is properly sourced and is perfectly okay for non circular orbits ("...the

111: 2242: 1536: 1461: 512:

forces. If only I knew how to explain that in the article without excessively confusing the average reader...

618: 3891: 759: 533: 467: 4175: 4127: 4088: 4068: 4037: 4001: 3790: 1931: 1905: 1739: 1721: 1618: 1592: 1395: 1337: 1038:

and such mnemonics, being infinite in possible number, can't be included unless they're in very common use.

610: 525: 302: 294: 103: 77: 4222: 2518: 2318: 2255: 1403: 1345: 882: 85: 47: 17: 2743: 2197: 2162: 2147: 2098: 2028: 1984: 1878: 1864: 1834: 1822: 1779: 1754: 1693: 1613:

It should either be removed completely or transferred to the centrifugal force and Coriolis force pages.

1079: 333: 549: 4171: 4123: 4084: 4064: 4033: 3997: 1927: 1901: 1735: 1717: 1614: 1588: 1519: 1502: 1399: 1341: 992: 986: 985:, the derivation had a misconception that might have confused some readers. The kinetic energy is a 598: 513: 480: 381: 279: 3949: 1391:

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

4102:

center of curvature of the path"). If you have a source that defines centripetal force as being a "

3953: 1075: 399: 220: 1421: 4161:

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

2212: 2181: 2131: 2114: 2063: 2048: 2006: 1951: 1671: 1477: 128: 4153:

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

4154: 4028: 1966: 1826: 1658: 1498: 1217: 1123: 694: 649: 505: 228: 3841: 2193: 2158: 2143: 2094: 2024: 1980: 1874: 1860: 1830: 1818: 1775: 1750: 1689: 1551: 501: 4047:

I think the section is well balanced and doesn't need re-wording, so I propose to keep it.

3972: 2469: 580: 2918: 2891: 2737:

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

1683: 792: 319: 3964: 4195: 4179: 4147: 4131: 4115: 4092: 4072: 4056: 4041: 4020: 4005: 3984: 2588: 2562: 2246: 2216: 2201: 2185: 2166: 2151: 2135: 2118: 2102: 2067: 2052: 2032: 2010: 1988: 1955: 1935: 1909: 1882: 1868: 1838: 1783: 1758: 1743: 1725: 1697: 1622: 1596: 1555: 1540: 1522: 1505: 1481: 1465: 1451: 1438: 1288: 1263: 1247: 1220: 1172: 1083: 652: 622: 601: 537: 522:"real" as a force that appears from an internal reference frame (ie centripetal force) 516: 487: 306: 270: 132: 115: 89: 4191: 4143: 4111: 4052: 4016: 3980: 1961:

I have added a source to the already provided source suggesting that centripetal force

1448: 1435: 1367: 1270: 1260: 1043: 1031: 509: 3968: 2495: 2370: 2173: 772: 4011:

I think the content you removed was relevant and properly sourced, so I restored it.

2208: 2177: 2127: 2110: 2059: 2044: 2002: 1947: 1926:

Coriolis force can produce a real effect. I'm hoping to read that paper maybe today.

1493: 1473: 560:

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

124: 242:

by the person who needs to be explained how the centripetal/centrifugal forces work

1285: 1244: 1213: 1169: 1133: 1119: 1047: 690: 645: 157: 144: 500:

The article claims that centripetal force is always a real force (as opposed to a

163:

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

4221:

If you wish to start a new discussion or revive an old one, please do so on the

1547: 1259:

get the logic behind this choice of heading. In what way is the formula basic?

46:

If you wish to start a new discussion or revive an old one, please do so on the

3244:

Adding the acceleration vector magnitudes to get total acceleration magnitude:

2058:

for me to work on incrementally without knowing what sources it is following.

3779:{\displaystyle |a|^{2}={\frac {v^{4}}{r^{2}}}\left(\sin ^{2}+\cos ^{2}\right)} 1919: 1302:"The centripetal force is the external force required to make a body follow a 326: 267: 4187: 4139: 4107: 4048: 4012: 3976: 1501:, which strongly suggests that it adds very little meaning to the article. – 1716:

When the two are not balanced, we get an ellipse, parabola, or hyperbola.

1900:

tension is transmitted directly through the centre of mass of the yo-yo.

1362:

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

4106:" then please present it. Otherwise I think this inquiry is off-topic. 202: 151: 1019: 2367:

Equations for uniform circular motion in terms of an arbitrary time

1829:" that avoids the issue, but a frontal attack would be interesting. 989:, i.e., a quantity with no direction, whereas the centripetal force 1997:

Well, probably you're right, but there are quite a few books (like

689:

gravity, and inertia codified in Newton's three laws of motion.) --

2611:

This will be the case if the arguments in the cos and sin equal 1

666:

Centripetal force must not be confused with central force either.

227:

from the 'orbit', so in this context, by default there is only a

681:

It seems to me that 'centripetal' only says something about the

2888:

Take second derivatives with respect to t to get accelerations

339: 4200: 4104:

force which acts towards the fixed centre of a rotating system

3963:

Hi, I have reverted your edits. Please have a careful look at

25: 2456:{\displaystyle x=r\cos(b)\quad \quad \quad \quad y=r\sin(b)} 232:

conventionally call the force keeping the object 'in orbit'.

1103:

Centripetal force should not be confused with central force

569: 368:

manifests itself when there is actual change of velocity.

2251: 705: 360:

manifests itself when there is actual change of velocity.

1428:

right would not have velocities or accelerations at the

1094:

The expressions 'centripetal force' and 'central force'_2

1233:

to its path (and increases its speed) and that which is

1657:. Sausalito CA: University Science Books. p. pp.28-29. 1515: 659:

The expressions 'centripetal force' and 'central force'

371:

The centrifugal manifestation of inertia is present in

340:

If it's present in one frame it's present in all frames

2172:

I think you're expressing a variant interpretation of

1093: 966:{\displaystyle -\mathbf {r} \cdot \mathbf {F} _{c}=2T} 924:. One may also use the more general vector equation 748:{\displaystyle -\mathbf {r} \cdot \mathbf {F} _{c}=2T} 3894: 3844: 3793: 3695: 3535: 3351: 3253: 2950: 2921: 2894: 2790: 2746: 2623: 2591: 2565: 2521: 2498: 2472: 2396: 2373: 2321: 2258: 995: 930: 885: 826: 795: 775: 712: 583: 658: 1118:

My intention is to edit the article accordingly. --

3933: 3879: 3829: 3778: 3680: 3520: 3336: 3233: 2934: 2907: 2877: 2770: 2726: 2603: 2577: 2548: 2504: 2484: 2455: 2379: 2352: 2289: 1825:) 15:50, 30 June 2008 (UTC) I've added a section " 1010: 965: 916: 867: 808: 781: 747: 589: 2176:. I prefer a more conventional interpretation. 973:, since the centripetal force is always directed 2237:different names depending on frame of reference. 1098:I repeat a question that I asked a year earlier 3337:{\displaystyle |a|^{2}=|a_{x}|^{2}+|a_{y}|^{2}} 2312:The derivation of the commonly cited equation: 1375:With a final sentence of whichever is correct: 1873:I've taken a stab at rewriting this example. 1605:The so-called derivation in polar coordinates 879:from which one may derive the desired result 8: 1801:. For example, the arc length and θ satisfy 1325:An elliptical orbit is not at constant speed 1202:of the shape of the orbit that is sustained. 1036:Knowledge (XXG) is not a collection of facts 868:{\displaystyle mv^{2}\equiv 2T\equiv rF_{c}} 548:This comment was inserted in the article by 1310:. The force is directed inward, toward the 1168:Hoping that this clarifies the difference, 283:reader. Misconceptions need to be adressed. 2300: 3920: 3914: 3903: 3895: 3893: 3872: 3864: 3853: 3845: 3843: 3816: 3810: 3802: 3794: 3792: 3765: 3752: 3735: 3725: 3719: 3710: 3705: 3696: 3694: 3654: 3641: 3615: 3602: 3585: 3575: 3569: 3563: 3550: 3545: 3536: 3534: 3510: 3500: 3494: 3475: 3462: 3452: 3437: 3427: 3421: 3402: 3389: 3379: 3366: 3361: 3352: 3350: 3328: 3323: 3316: 3307: 3298: 3293: 3286: 3277: 3268: 3263: 3254: 3252: 3223: 3213: 3207: 3188: 3150: 3128: 3114: 3108: 3099: 3079: 3069: 3063: 3044: 3006: 2984: 2970: 2964: 2955: 2949: 2926: 2920: 2899: 2893: 2856: 2810: 2789: 2753: 2745: 2697: 2643: 2622: 2590: 2564: 2528: 2520: 2497: 2471: 2395: 2372: 2338: 2328: 2320: 2275: 2265: 2257: 1002: 997: 994: 948: 943: 934: 929: 899: 890: 884: 859: 834: 825: 800: 794: 774: 730: 725: 716: 711: 582: 977:to the radius vector in circular motion. 3934:{\displaystyle |F|=m{\frac {v^{2}}{r}}} 1967:Centripetal_force#General_planar_motion 1146:on the distance between the two bodies 789:and the magnitude of centripetal force 584: 4219:Do not edit the contents of this page. 3830:{\displaystyle |a|={\frac {v^{2}}{r}}} 1679: 1669: 44:Do not edit the contents of this page. 2549:{\displaystyle b={\frac {2\pi r}{v}}} 2353:{\displaystyle F={\frac {mv^{2}}{r}}} 2290:{\displaystyle F={\frac {mv^{2}}{r}}} 1357:Clarification of Solid Object Example 917:{\displaystyle F_{c}={\frac {2T}{r}}} 7: 2771:{\displaystyle t={\frac {b}{2\pi }}} 1034:, a related result. Unfortunately, 4078:The Definition of Centripetal Force 1492:for a force to exist, such as e.g. 210:for the purpose of Knowledge (XXG) 24: 1065:though since I'm not sure. Adios 456:may change in the transformation. 4204: 1420: 1112:directed towards the same spot. 1011:{\displaystyle \mathbf {F} _{c}} 998: 944: 935: 726: 717: 29: 2512:, one revolution occurs when: 2466:The circumference of circle is 2252:Clear and Simple derivation of 1789:Local coordinates and curvature 1638:). All that is done is to find 1366:" For a solid spinning object, 177:In the case of circular motion 3904: 3896: 3873: 3865: 3854: 3846: 3803: 3795: 3706: 3697: 3546: 3537: 3362: 3353: 3324: 3308: 3294: 3278: 3264: 3255: 2450: 2444: 2418: 2412: 2085:occur in verbal descriptions. 1322:What about an elliptical path? 1: 3093: 3091: 3089: 3087: 2835: 2833: 2831: 2829: 2676: 2674: 2672: 2670: 2427: 2425: 2423: 2421: 2038:Sources and other work needed 1523:01:18, 23 December 2007 (UTC) 1506:22:37, 22 December 2007 (UTC) 1482:13:02, 10 December 2007 (UTC) 1238:centripetal force is applied 1101:In the article it is stated: 517:16:20, 24 December 2005 (UTC) 344:In the article it is stated: 307:03:53, 22 February 2008 (UTC) 4196:20:12, 6 November 2010 (UTC) 4180:20:01, 6 November 2010 (UTC) 4148:16:41, 6 November 2010 (UTC) 4132:15:07, 6 November 2010 (UTC) 4116:11:46, 6 November 2010 (UTC) 4093:11:14, 6 November 2010 (UTC) 4073:00:49, 5 November 2010 (UTC) 4057:23:05, 4 November 2010 (UTC) 4042:22:59, 4 November 2010 (UTC) 4021:22:48, 4 November 2010 (UTC) 4006:22:42, 4 November 2010 (UTC) 3991:Sources of centripetal force 3985:21:06, 18 October 2010 (UTC) 3958:18:23, 18 October 2010 (UTC) 1936:04:59, 20 January 2009 (UTC) 1910:04:52, 20 January 2009 (UTC) 1883:23:02, 19 January 2009 (UTC) 1869:20:56, 19 January 2009 (UTC) 1289:12:11, 3 February 2007 (UTC) 1264:03:38, 3 February 2007 (UTC) 1248:18:50, 3 February 2007 (UTC) 1221:18:22, 3 February 2007 (UTC) 1173:12:25, 3 February 2007 (UTC) 1127:01:15, 23 January 2007 (UTC) 1084:04:15, 6 February 2009 (UTC) 698:10:20, 4 February 2006 (UTC) 663:In the article it is stated: 653:10:02, 4 February 2006 (UTC) 2614:Applying this constraint: 1651:John Robert Taylor (2005). 602:22:31, 1 January 2006 (UTC) 488:09:11, 26 August 2005 (UTC) 403:11:52, 25 August 2005 (UTC) 4255: 1452:03:17, 16 March 2007 (UTC) 1439:00:52, 16 March 2007 (UTC) 623:20:35, 26 March 2008 (UTC) 322:21:59, May 16, 2004 (UTC) 2247:15:17, 29 July 2010 (UTC) 2226:Better simple definition? 2217:04:37, 23 June 2009 (UTC) 2202:00:07, 23 June 2009 (UTC) 2186:04:37, 23 June 2009 (UTC) 2167:00:00, 23 June 2009 (UTC) 2152:23:55, 22 June 2009 (UTC) 2136:22:08, 22 June 2009 (UTC) 2119:22:01, 22 June 2009 (UTC) 2103:18:13, 22 June 2009 (UTC) 2068:06:07, 23 June 2009 (UTC) 2053:16:04, 21 June 2009 (UTC) 1516:went ahead and deleted it 538:08:57, 3 April 2008 (UTC) 388:23:40, 13 Mar 2005 (UTC) 376:a change of perspective. 336:17:28, 28 Oct 2004 (UTC) 329:15:44, 17 Oct 2004 (UTC) 133:05:57, 23 June 2009 (UTC) 116:19:48, 10 June 2009 (UTC) 90:17:27, 23 July 2010 (UTC) 3880:{\displaystyle |F|=m|a|} 2033:18:47, 9 June 2009 (UTC) 2011:00:53, 9 June 2009 (UTC) 1989:16:23, 6 June 2009 (UTC) 1979:of non-technical usage. 1956:14:09, 5 June 2009 (UTC) 1839:03:43, 2 July 2008 (UTC) 1784:17:55, 15 May 2008 (UTC) 1759:12:54, 22 May 2008 (UTC) 1744:04:39, 12 May 2008 (UTC) 1726:04:24, 12 May 2008 (UTC) 1698:14:20, 11 May 2008 (UTC) 1623:08:32, 11 May 2008 (UTC) 1597:04:33, 12 May 2008 (UTC) 1575:electrostatics, or from 1556:16:27, 11 May 2008 (UTC) 1417:== Diagram is wrong? == 1051:07:51, 9 July 2006 (UTC) 706:Reasons for deleting of 468:gravitational slingshots 412:what I almost always do. 353:That doesn't make sense. 271:21:57, 14 May 2004 (UTC) 1541:16:34, 5 May 2008 (UTC) 1466:16:34, 5 May 2008 (UTC) 3935: 3881: 3831: 3780: 3682: 3522: 3338: 3235: 2936: 2909: 2879: 2772: 2728: 2605: 2579: 2550: 2506: 2486: 2485:{\displaystyle 2\pi r} 2457: 2381: 2354: 2291: 1514:On further thought, I 1194:My question is: is it 1142:functional dependence 1012: 967: 918: 869: 810: 783: 749: 591: 590:{\displaystyle \hbar } 166:The force equation is 96:Forgetting the basics? 18:Talk:Centripetal force 4217:of past discussions. 3936: 3882: 3832: 3781: 3683: 3523: 3339: 3236: 2937: 2935:{\displaystyle a_{y}} 2910: 2908:{\displaystyle a_{x}} 2880: 2773: 2729: 2606: 2580: 2551: 2507: 2492:so given a velocity, 2487: 2458: 2382: 2355: 2292: 1013: 968: 919: 870: 811: 809:{\displaystyle F_{c}} 784: 750: 592: 139:Changing acceleration 42:of past discussions. 3892: 3842: 3791: 3693: 3533: 3349: 3251: 2948: 2919: 2892: 2788: 2744: 2621: 2589: 2563: 2519: 2496: 2470: 2394: 2371: 2319: 2256: 1610:centripetal force. 1312:center of the circle 993: 928: 883: 824: 793: 773: 710: 581: 496:Always a real force? 70:Roller coaster error 2604:{\displaystyle y=0} 2578:{\displaystyle x=r} 1854:Classical Mechanics 1851:Nonsmooth Mechanics 1654:Classical Mechanics 249:in the introduction 221:Newtonian mechanics 3931: 3877: 3827: 3776: 3678: 3518: 3334: 3231: 3094: 3092: 3090: 3088: 2932: 2905: 2875: 2836: 2834: 2832: 2830: 2768: 2724: 2677: 2675: 2673: 2671: 2601: 2575: 2546: 2502: 2482: 2453: 2428: 2426: 2424: 2422: 2377: 2350: 2287: 1827:Alternative Method 1008: 963: 914: 865: 806: 779: 745: 587: 4242: 4241: 4229: 4228: 4223:current talk page 4168:centripetal force 4155:centrifugal force 4029:centrifugal force 3946: 3945: 3929: 3825: 3741: 3667: 3628: 3591: 3516: 3488: 3443: 3415: 3229: 3201: 3163: 3135: 3085: 3057: 3019: 2991: 2869: 2823: 2766: 2718: 2664: 2544: 2505:{\displaystyle v} 2380:{\displaystyle b} 2348: 2285: 1857:Predicting Motion 1499:centrifugal force 1411: 1398:comment added by 1353: 1340:comment added by 1299:The article has: 1295:Elliptical Paths? 912: 816:give the equation 782:{\displaystyle T} 625: 613:comment added by 550:User:67.71.37.250 540: 528:comment added by 309: 297:comment added by 229:centrifugal force 106:comment added by 80:comment added by 67: 66: 54: 53: 48:current talk page 4246: 4238: 4231: 4230: 4208: 4207: 4201: 4163:John Blackburne 3940: 3938: 3937: 3932: 3930: 3925: 3924: 3915: 3907: 3899: 3886: 3884: 3883: 3878: 3876: 3868: 3857: 3849: 3836: 3834: 3833: 3828: 3826: 3821: 3820: 3811: 3806: 3798: 3785: 3783: 3782: 3777: 3775: 3771: 3770: 3769: 3757: 3756: 3742: 3740: 3739: 3730: 3729: 3720: 3715: 3714: 3709: 3700: 3687: 3685: 3684: 3679: 3677: 3673: 3672: 3668: 3663: 3655: 3646: 3645: 3633: 3629: 3624: 3616: 3607: 3606: 3592: 3590: 3589: 3580: 3579: 3570: 3568: 3567: 3555: 3554: 3549: 3540: 3527: 3525: 3524: 3519: 3517: 3515: 3514: 3505: 3504: 3495: 3493: 3489: 3484: 3476: 3467: 3466: 3457: 3456: 3444: 3442: 3441: 3432: 3431: 3422: 3420: 3416: 3411: 3403: 3394: 3393: 3384: 3383: 3371: 3370: 3365: 3356: 3343: 3341: 3340: 3335: 3333: 3332: 3327: 3321: 3320: 3311: 3303: 3302: 3297: 3291: 3290: 3281: 3273: 3272: 3267: 3258: 3240: 3238: 3237: 3232: 3230: 3228: 3227: 3218: 3217: 3208: 3206: 3202: 3197: 3189: 3168: 3164: 3159: 3151: 3136: 3134: 3133: 3132: 3119: 3118: 3109: 3104: 3103: 3086: 3084: 3083: 3074: 3073: 3064: 3062: 3058: 3053: 3045: 3024: 3020: 3015: 3007: 2992: 2990: 2989: 2988: 2975: 2974: 2965: 2960: 2959: 2941: 2939: 2938: 2933: 2931: 2930: 2914: 2912: 2911: 2906: 2904: 2903: 2884: 2882: 2881: 2876: 2874: 2870: 2865: 2857: 2828: 2824: 2819: 2811: 2777: 2775: 2774: 2769: 2767: 2765: 2754: 2733: 2731: 2730: 2725: 2723: 2719: 2717: 2706: 2698: 2669: 2665: 2663: 2652: 2644: 2610: 2608: 2607: 2602: 2584: 2582: 2581: 2576: 2555: 2553: 2552: 2547: 2545: 2540: 2529: 2511: 2509: 2508: 2503: 2491: 2489: 2488: 2483: 2462: 2460: 2459: 2454: 2386: 2384: 2383: 2378: 2359: 2357: 2356: 2351: 2349: 2344: 2343: 2342: 2329: 2305:Extended content 2301: 2296: 2294: 2293: 2288: 2286: 2281: 2280: 2279: 2266: 1687: 1682:has extra text ( 1681: 1677: 1675: 1667: 1424: 1393: 1335: 1017: 1015: 1014: 1009: 1007: 1006: 1001: 972: 970: 969: 964: 953: 952: 947: 938: 923: 921: 920: 915: 913: 908: 900: 895: 894: 874: 872: 871: 866: 864: 863: 839: 838: 815: 813: 812: 807: 805: 804: 788: 786: 785: 780: 754: 752: 751: 746: 735: 734: 729: 720: 608: 596: 594: 593: 588: 523: 502:fictitious force 349:rotating frames. 292: 118: 92: 63: 56: 55: 33: 32: 26: 4254: 4253: 4249: 4248: 4247: 4245: 4244: 4243: 4234: 4205: 4080: 3993: 3947: 3916: 3890: 3889: 3840: 3839: 3812: 3789: 3788: 3761: 3748: 3747: 3743: 3731: 3721: 3704: 3691: 3690: 3656: 3650: 3637: 3617: 3611: 3598: 3597: 3593: 3581: 3571: 3559: 3544: 3531: 3530: 3506: 3496: 3477: 3471: 3458: 3448: 3433: 3423: 3404: 3398: 3385: 3375: 3360: 3347: 3346: 3322: 3312: 3292: 3282: 3262: 3249: 3248: 3219: 3209: 3190: 3184: 3152: 3146: 3124: 3120: 3110: 3095: 3075: 3065: 3046: 3040: 3008: 3002: 2980: 2976: 2966: 2951: 2946: 2945: 2922: 2917: 2916: 2895: 2890: 2889: 2858: 2852: 2812: 2806: 2786: 2785: 2758: 2742: 2741: 2707: 2699: 2693: 2653: 2645: 2639: 2619: 2618: 2587: 2586: 2561: 2560: 2530: 2517: 2516: 2494: 2493: 2468: 2467: 2392: 2391: 2369: 2368: 2334: 2330: 2317: 2316: 2306: 2298: 2271: 2267: 2254: 2253: 2228: 2075: 2040: 1943: 1846: 1809:, for example, 1791: 1771: 1678: 1668: 1664: 1650: 1607: 1520:Henning Makholm 1503:Henning Makholm 1359: 1297: 1256: 1096: 1058: 996: 991: 990: 942: 926: 925: 901: 886: 881: 880: 855: 830: 822: 821: 796: 791: 790: 771: 770: 756: 724: 708: 707: 661: 631: 599:Henning Makholm 579: 578: 546: 514:Henning Makholm 498: 481:Cleon Teunissen 382:Cleon Teunissen 342: 280:Cleon Teunissen 141: 108:209.195.102.103 101: 98: 75: 72: 59: 30: 22: 21: 20: 12: 11: 5: 4252: 4250: 4240: 4239: 4227: 4226: 4209: 4199: 4198: 4151: 4150: 4119: 4118: 4079: 4076: 4060: 4059: 4024: 4023: 3992: 3989: 3988: 3987: 3944: 3943: 3942: 3941: 3928: 3923: 3919: 3913: 3910: 3906: 3902: 3898: 3887: 3875: 3871: 3867: 3863: 3860: 3856: 3852: 3848: 3837: 3824: 3819: 3815: 3809: 3805: 3801: 3797: 3786: 3774: 3768: 3764: 3760: 3755: 3751: 3746: 3738: 3734: 3728: 3724: 3718: 3713: 3708: 3703: 3699: 3688: 3676: 3671: 3666: 3662: 3659: 3653: 3649: 3644: 3640: 3636: 3632: 3627: 3623: 3620: 3614: 3610: 3605: 3601: 3596: 3588: 3584: 3578: 3574: 3566: 3562: 3558: 3553: 3548: 3543: 3539: 3528: 3513: 3509: 3503: 3499: 3492: 3487: 3483: 3480: 3474: 3470: 3465: 3461: 3455: 3451: 3447: 3440: 3436: 3430: 3426: 3419: 3414: 3410: 3407: 3401: 3397: 3392: 3388: 3382: 3378: 3374: 3369: 3364: 3359: 3355: 3344: 3331: 3326: 3319: 3315: 3310: 3306: 3301: 3296: 3289: 3285: 3280: 3276: 3271: 3266: 3261: 3257: 3242: 3241: 3226: 3222: 3216: 3212: 3205: 3200: 3196: 3193: 3187: 3183: 3180: 3177: 3174: 3171: 3167: 3162: 3158: 3155: 3149: 3145: 3142: 3139: 3131: 3127: 3123: 3117: 3113: 3107: 3102: 3098: 3082: 3078: 3072: 3068: 3061: 3056: 3052: 3049: 3043: 3039: 3036: 3033: 3030: 3027: 3023: 3018: 3014: 3011: 3005: 3001: 2998: 2995: 2987: 2983: 2979: 2973: 2969: 2963: 2958: 2954: 2929: 2925: 2902: 2898: 2886: 2885: 2873: 2868: 2864: 2861: 2855: 2851: 2848: 2845: 2842: 2839: 2827: 2822: 2818: 2815: 2809: 2805: 2802: 2799: 2796: 2793: 2781:which gives: 2779: 2778: 2764: 2761: 2757: 2752: 2749: 2735: 2734: 2722: 2716: 2713: 2710: 2705: 2702: 2696: 2692: 2689: 2686: 2683: 2680: 2668: 2662: 2659: 2656: 2651: 2648: 2642: 2638: 2635: 2632: 2629: 2626: 2600: 2597: 2594: 2574: 2571: 2568: 2559:At this point 2557: 2556: 2543: 2539: 2536: 2533: 2527: 2524: 2501: 2481: 2478: 2475: 2464: 2463: 2452: 2449: 2446: 2443: 2440: 2437: 2434: 2431: 2420: 2417: 2414: 2411: 2408: 2405: 2402: 2399: 2376: 2361: 2360: 2347: 2341: 2337: 2333: 2327: 2324: 2308: 2307: 2304: 2299: 2297: 2284: 2278: 2274: 2270: 2264: 2261: 2250: 2239:67.167.249.170 2227: 2224: 2222: 2220: 2219: 2189: 2188: 2139: 2138: 2122: 2121: 2074: 2071: 2039: 2036: 2016: 2015: 2014: 2013: 1992: 1991: 1971: 1970: 1942: 1939: 1915: 1914: 1913: 1912: 1894: 1893: 1892: 1891: 1845: 1842: 1790: 1787: 1770: 1767: 1766: 1765: 1764: 1763: 1762: 1761: 1703: 1702: 1701: 1700: 1662: 1606: 1603: 1602: 1601: 1600: 1599: 1569: 1568: 1567: 1566: 1559: 1558: 1533:71.251.176.164 1528: 1527: 1526: 1525: 1509: 1508: 1458:71.251.176.164 1456: 1368:tensile stress 1358: 1355: 1333: 1332: 1329: 1326: 1323: 1317: 1308:constant speed 1296: 1293: 1292: 1291: 1281: 1280: 1275: 1274: 1255: 1252: 1251: 1250: 1226: 1225: 1224: 1223: 1206: 1205: 1204: 1203: 1199: 1189: 1188: 1187: 1186: 1183: 1176: 1175: 1165: 1164: 1138: 1137: 1095: 1092: 1091: 1089: 1067: 1057: 1054: 1044:virial theorem 1040: 1039: 1032:virial theorem 1024: 1023: 1005: 1000: 979: 978: 962: 959: 956: 951: 946: 941: 937: 933: 911: 907: 904: 898: 893: 889: 876: 875: 862: 858: 854: 851: 848: 845: 842: 837: 833: 829: 818: 817: 803: 799: 778: 755: 744: 741: 738: 733: 728: 723: 719: 715: 704: 702: 664: 660: 657: 656: 655: 640: 639: 630: 627: 586: 566: 565: 564: 563: 562: 561: 545: 542: 497: 494: 493: 492: 491: 490: 474: 473: 472: 471: 460: 459: 458: 457: 446: 445: 444: 443: 436: 435: 434: 433: 426: 425: 424: 423: 416: 415: 414: 413: 406: 405: 400:Themissinglint 354: 351: 350: 341: 338: 311: 310: 287: 286: 285: 284: 274: 273: 253: 252: 236: 235: 234: 233: 214: 213: 161: 140: 137: 136: 135: 97: 94: 71: 68: 65: 64: 52: 51: 34: 23: 15: 14: 13: 10: 9: 6: 4: 3: 2: 4251: 4237: 4233: 4232: 4224: 4220: 4216: 4215: 4210: 4203: 4202: 4197: 4193: 4189: 4184: 4183: 4182: 4181: 4177: 4173: 4169: 4164: 4162: 4158: 4156: 4149: 4145: 4141: 4136: 4135: 4134: 4133: 4129: 4125: 4117: 4113: 4109: 4105: 4101: 4100:instantaneous 4097: 4096: 4095: 4094: 4090: 4086: 4077: 4075: 4074: 4070: 4066: 4058: 4054: 4050: 4046: 4045: 4044: 4043: 4039: 4035: 4030: 4022: 4018: 4014: 4010: 4009: 4008: 4007: 4003: 3999: 3990: 3986: 3982: 3978: 3974: 3970: 3966: 3962: 3961: 3960: 3959: 3955: 3951: 3926: 3921: 3917: 3911: 3908: 3900: 3888: 3869: 3861: 3858: 3850: 3838: 3822: 3817: 3813: 3807: 3799: 3787: 3772: 3766: 3762: 3758: 3753: 3749: 3744: 3736: 3732: 3726: 3722: 3716: 3711: 3701: 3689: 3674: 3669: 3664: 3660: 3657: 3651: 3647: 3642: 3638: 3634: 3630: 3625: 3621: 3618: 3612: 3608: 3603: 3599: 3594: 3586: 3582: 3576: 3572: 3564: 3560: 3556: 3551: 3541: 3529: 3511: 3507: 3501: 3497: 3490: 3485: 3481: 3478: 3472: 3468: 3463: 3459: 3453: 3449: 3445: 3438: 3434: 3428: 3424: 3417: 3412: 3408: 3405: 3399: 3395: 3390: 3386: 3380: 3376: 3372: 3367: 3357: 3345: 3329: 3317: 3313: 3304: 3299: 3287: 3283: 3274: 3269: 3259: 3247: 3246: 3245: 3224: 3220: 3214: 3210: 3203: 3198: 3194: 3191: 3185: 3181: 3178: 3175: 3172: 3169: 3165: 3160: 3156: 3153: 3147: 3143: 3140: 3137: 3129: 3125: 3121: 3115: 3111: 3105: 3100: 3096: 3080: 3076: 3070: 3066: 3059: 3054: 3050: 3047: 3041: 3037: 3034: 3031: 3028: 3025: 3021: 3016: 3012: 3009: 3003: 2999: 2996: 2993: 2985: 2981: 2977: 2971: 2967: 2961: 2956: 2952: 2944: 2943: 2942: 2927: 2923: 2900: 2896: 2871: 2866: 2862: 2859: 2853: 2849: 2846: 2843: 2840: 2837: 2825: 2820: 2816: 2813: 2807: 2803: 2800: 2797: 2794: 2791: 2784: 2783: 2782: 2762: 2759: 2755: 2750: 2747: 2740: 2739: 2738: 2720: 2714: 2711: 2708: 2703: 2700: 2694: 2690: 2687: 2684: 2681: 2678: 2666: 2660: 2657: 2654: 2649: 2646: 2640: 2636: 2633: 2630: 2627: 2624: 2617: 2616: 2615: 2612: 2598: 2595: 2592: 2572: 2569: 2566: 2541: 2537: 2534: 2531: 2525: 2522: 2515: 2514: 2513: 2499: 2479: 2476: 2473: 2447: 2441: 2438: 2435: 2432: 2429: 2415: 2409: 2406: 2403: 2400: 2397: 2390: 2389: 2388: 2374: 2365: 2345: 2339: 2335: 2331: 2325: 2322: 2315: 2314: 2313: 2310: 2309: 2303: 2302: 2282: 2276: 2272: 2268: 2262: 2259: 2249: 2248: 2244: 2240: 2234: 2231: 2225: 2223: 2218: 2214: 2210: 2206: 2205: 2204: 2203: 2199: 2195: 2187: 2183: 2179: 2175: 2171: 2170: 2169: 2168: 2164: 2160: 2154: 2153: 2149: 2145: 2137: 2133: 2129: 2124: 2123: 2120: 2116: 2112: 2107: 2106: 2105: 2104: 2100: 2096: 2090: 2086: 2082: 2081:authorship. 2078: 2072: 2070: 2069: 2065: 2061: 2055: 2054: 2050: 2046: 2037: 2035: 2034: 2030: 2026: 2022: 2012: 2008: 2004: 2000: 1996: 1995: 1994: 1993: 1990: 1986: 1982: 1978: 1973: 1972: 1968: 1964: 1960: 1959: 1958: 1957: 1953: 1949: 1940: 1938: 1937: 1933: 1929: 1923: 1921: 1911: 1907: 1903: 1898: 1897: 1896: 1895: 1889: 1888: 1887: 1886: 1885: 1884: 1880: 1876: 1871: 1870: 1866: 1862: 1858: 1855: 1852: 1844:Yo-yo example 1843: 1841: 1840: 1836: 1832: 1828: 1824: 1820: 1816: 1812: 1808: 1804: 1800: 1797:and location 1796: 1788: 1786: 1785: 1781: 1777: 1768: 1760: 1756: 1752: 1747: 1746: 1745: 1741: 1737: 1732: 1731: 1730: 1729: 1728: 1727: 1723: 1719: 1714: 1710: 1707: 1699: 1695: 1691: 1685: 1673: 1665: 1660: 1656: 1655: 1648: 1644: 1641: 1637: 1633: 1629: 1628: 1627: 1626: 1625: 1624: 1620: 1616: 1611: 1604: 1598: 1594: 1590: 1586: 1582: 1578: 1573: 1572: 1571: 1570: 1563: 1562: 1561: 1560: 1557: 1553: 1549: 1545: 1544: 1543: 1542: 1538: 1534: 1524: 1521: 1517: 1513: 1512: 1511: 1510: 1507: 1504: 1500: 1495: 1494:Lorentz force 1491: 1486: 1485: 1484: 1483: 1479: 1475: 1469: 1467: 1463: 1459: 1454: 1453: 1450: 1445: 1441: 1440: 1437: 1432: 1429: 1425: 1423: 1418: 1416: 1412: 1409: 1405: 1401: 1397: 1392: 1388: 1385: 1384: 1380: 1377: 1376: 1372: 1369: 1364: 1363: 1356: 1354: 1351: 1347: 1343: 1339: 1330: 1327: 1324: 1321: 1320: 1319: 1315: 1313: 1309: 1305: 1304:circular path 1300: 1294: 1290: 1287: 1283: 1282: 1277: 1276: 1272: 1268: 1267: 1266: 1265: 1262: 1253: 1249: 1246: 1241: 1236: 1235:perpendicular 1232: 1228: 1227: 1222: 1219: 1215: 1210: 1209: 1208: 1207: 1200: 1197: 1193: 1192: 1191: 1190: 1184: 1180: 1179: 1178: 1177: 1174: 1171: 1167: 1166: 1162: 1157: 1153: 1149: 1145: 1140: 1139: 1135: 1131: 1130: 1129: 1128: 1125: 1121: 1116: 1113: 1109: 1105: 1104: 1099: 1090: 1087: 1085: 1081: 1077: 1071: 1066: 1062: 1055: 1053: 1052: 1049: 1045: 1037: 1033: 1029: 1026: 1025: 1021: 1003: 988: 984: 981: 980: 976: 960: 957: 954: 949: 939: 931: 909: 905: 902: 896: 891: 887: 878: 877: 860: 856: 852: 849: 846: 843: 840: 835: 831: 827: 820: 819: 801: 797: 776: 768: 765: 764: 763: 761: 742: 739: 736: 731: 721: 713: 703: 700: 699: 696: 692: 686: 684: 679: 675: 671: 668: 667: 654: 651: 647: 642: 641: 636: 635: 634: 628: 626: 624: 620: 616: 615:71.232.14.193 612: 604: 603: 600: 576: 571: 559: 558: 557: 556: 555: 554: 553: 551: 543: 541: 539: 535: 531: 527: 519: 518: 515: 511: 507: 503: 495: 489: 486: 482: 478: 477: 476: 475: 469: 464: 463: 462: 461: 455: 450: 449: 448: 447: 440: 439: 438: 437: 430: 429: 428: 427: 420: 419: 418: 417: 410: 409: 408: 407: 404: 401: 396: 391: 390: 389: 387: 383: 377: 374: 369: 367: 361: 359: 347: 346: 345: 337: 335: 334:134.153.18.39 330: 328: 323: 321: 317: 308: 304: 300: 296: 289: 288: 281: 278: 277: 276: 275: 272: 269: 264: 259: 255: 254: 250: 246: 245: 238: 237: 230: 226: 222: 218: 217: 216: 215: 211: 207: 206: 205: 204: 198: 196: 192: 188: 184: 180: 175: 173: 169: 164: 160: 159: 154: 153: 147: 146: 138: 134: 130: 126: 121: 120: 119: 117: 113: 109: 105: 95: 93: 91: 87: 83: 79: 69: 62: 58: 57: 49: 45: 41: 40: 35: 28: 27: 19: 4235: 4218: 4212: 4167: 4166:Yet here at 4165: 4160: 4159: 4152: 4120: 4103: 4099: 4081: 4061: 4025: 3994: 3948: 3243: 2887: 2780: 2736: 2613: 2558: 2465: 2366: 2362: 2311: 2235: 2232: 2229: 2221: 2190: 2155: 2140: 2091: 2087: 2083: 2079: 2076: 2056: 2041: 2017: 1962: 1944: 1924: 1916: 1872: 1847: 1814: 1810: 1806: 1802: 1798: 1794: 1792: 1772: 1715: 1711: 1708: 1704: 1653: 1646: 1642: 1639: 1635: 1631: 1612: 1608: 1584: 1580: 1576: 1529: 1489: 1470: 1455: 1446: 1442: 1433: 1430: 1426: 1419: 1414: 1413: 1390: 1389: 1386: 1382: 1381: 1378: 1374: 1373: 1365: 1361: 1360: 1334: 1316: 1311: 1307: 1303: 1301: 1298: 1257: 1239: 1234: 1230: 1195: 1160: 1155: 1151: 1147: 1143: 1117: 1114: 1110: 1106: 1102: 1100: 1097: 1088: 1072: 1068: 1063: 1059: 1056:small change 1041: 1027: 982: 974: 766: 757: 701: 687: 682: 680: 676: 672: 669: 665: 662: 638:interaction. 632: 605: 574: 567: 547: 530:84.71.66.130 520: 499: 453: 394: 378: 372: 370: 365: 362: 357: 352: 343: 331: 324: 315: 312: 262: 257: 248: 243: 241: 224: 209: 199: 194: 190: 186: 182: 178: 176: 171: 167: 165: 162: 155: 148: 142: 99: 82:67.183.23.68 73: 60: 43: 37: 4211:This is an 4172:David Tombe 4124:David Tombe 4085:David Tombe 4065:David Tombe 4034:David Tombe 3998:David Tombe 3975:. Cheers - 2194:Brews ohare 2159:Brews ohare 2144:Brews ohare 2095:Brews ohare 2073:Symbol-soup 2025:Brews ohare 1981:Brews ohare 1941:Definition? 1928:David Tombe 1902:David Tombe 1875:Brews ohare 1861:Brews ohare 1831:Brews ohare 1819:Brews ohare 1776:Brews ohare 1751:Brews ohare 1736:David Tombe 1718:David Tombe 1690:Brews ohare 1615:David Tombe 1589:David Tombe 1394:—Preceding 1336:—Preceding 609:—Preceding 524:—Preceding 506:centrifugal 454:represented 314:reference. 299:18.202.1.85 293:—Preceding 244:intuitively 240:understand 189:=-m v^2/r^2 102:—Preceding 76:—Preceding 36:This is an 1920:rattleback 1663:189138922X 1400:75.7.20.57 1342:75.7.44.72 320:AstroNomer 4236:Archive 1 3950:MaxLupton 1803:ds = ρ dθ 1769:Revisions 1672:cite book 1449:BlckKnght 1436:BlckKnght 1415:Bold text 1271:Rracecarr 1261:Rracecarr 1196:necessary 683:direction 223:teaches, 181:=-v^2/r^2 61:Archive 1 2209:Dicklyon 2178:Dicklyon 2128:Dicklyon 2111:Dicklyon 2060:Dicklyon 2045:Dicklyon 2021:entirely 2003:Dicklyon 1948:Dicklyon 1565:picture. 1474:Theaveng 1408:contribs 1396:unsigned 1350:contribs 1338:unsigned 1318:Issues: 1231:parallel 1076:GLeeDads 975:opposite 611:unsigned 526:unsigned 510:Coriolis 295:unsigned 125:Dicklyon 104:unsigned 78:unsigned 4214:archive 1977:example 1813:= 0.5 1713:force. 1254:Heading 1214:Cleonis 1134:Cleonis 1120:Cleonis 1048:WillowW 760:Utkarsh 691:Cleonis 646:Cleonis 629:Comment 577:and/or 158:Rjstott 145:Rjstott 39:archive 4157:that, 3973:wp:NOR 1963:always 1799:s + ds 1680:|page= 1548:SCZenz 1286:Willow 1245:Willow 1170:Willow 1020:vector 987:scalar 983:Second 185:, and 3965:wp:RS 1975:cute 1490:cause 1383:Or... 1028:Third 1018:is a 767:First 758:Dear 544:Units 327:Drw25 268:Gutza 258:feels 16:< 4192:talk 4188:DVdm 4176:talk 4144:talk 4140:DVdm 4128:talk 4112:talk 4108:DVdm 4089:talk 4069:talk 4053:talk 4049:DVdm 4038:talk 4017:talk 4013:DVdm 4002:talk 3981:talk 3977:DVdm 3971:and 3969:wp:V 3954:talk 2915:and 2585:and 2243:talk 2213:talk 2198:talk 2182:talk 2174:WP:V 2163:talk 2148:talk 2132:talk 2115:talk 2099:talk 2064:talk 2049:talk 2029:talk 2023:. 2007:talk 1999:this 1985:talk 1952:talk 1932:talk 1906:talk 1879:talk 1865:talk 1835:talk 1823:talk 1780:talk 1755:talk 1740:talk 1722:talk 1694:talk 1684:help 1659:ISBN 1619:talk 1593:talk 1552:talk 1537:talk 1478:talk 1462:talk 1404:talk 1346:talk 1240:only 1218:Talk 1144:only 1124:Talk 1080:talk 695:Talk 650:Talk 619:talk 534:talk 508:and 485:Talk 395:seem 386:Talk 373:both 366:only 358:only 303:talk 263:they 225:away 129:talk 112:talk 86:talk 3763:cos 3750:sin 3639:cos 3600:sin 3460:sin 3387:cos 3179:sin 3141:sin 3035:cos 2997:cos 2847:sin 2801:cos 2688:sin 2634:cos 2439:sin 2407:cos 1859:. 1807:not 1579:= q 1518:. – 1314:." 1306:at 1269:Hi 1132:Hi 442:is. 170:=m 4194:) 4178:) 4146:) 4130:) 4114:) 4091:) 4071:) 4055:) 4040:) 4019:) 4004:) 3983:) 3967:, 3956:) 3648:⁡ 3609:⁡ 3469:⁡ 3396:⁡ 3182:⁡ 3173:− 3144:⁡ 3038:⁡ 3029:− 3000:⁡ 2850:⁡ 2804:⁡ 2763:π 2712:π 2691:⁡ 2658:π 2637:⁡ 2535:π 2477:π 2442:⁡ 2410:⁡ 2387:: 2245:) 2215:) 2200:) 2184:) 2165:) 2150:) 2134:) 2117:) 2101:) 2066:) 2051:) 2031:) 2009:) 1987:) 1954:) 1934:) 1922:? 1908:) 1881:) 1867:) 1837:) 1815:dθ 1811:ds 1805:, 1782:) 1757:) 1742:) 1724:) 1696:) 1688:. 1676:: 1674:}} 1670:{{ 1647:dt 1645:/ 1634:( 1621:) 1595:) 1554:) 1539:) 1480:) 1464:) 1447:-- 1434:-- 1410:) 1406:• 1352:) 1348:• 1216:| 1212:-- 1122:| 1086:) 1082:) 940:⋅ 932:− 850:≡ 841:≡ 722:⋅ 714:− 693:| 648:| 621:) 585:ℏ 570:SI 552:: 536:) 483:| 384:| 380:-- 305:) 203:AN 201:-- 193:. 174:, 152:AN 150:-- 131:) 114:) 88:) 4225:. 4190:( 4174:( 4142:( 4126:( 4110:( 4087:( 4067:( 4051:( 4036:( 4015:( 4000:( 3979:( 3952:( 3927:r 3922:2 3918:v 3912:m 3909:= 3905:| 3901:F 3897:| 3874:| 3870:a 3866:| 3862:m 3859:= 3855:| 3851:F 3847:| 3823:r 3818:2 3814:v 3808:= 3804:| 3800:a 3796:| 3773:) 3767:2 3759:+ 3754:2 3745:( 3737:2 3733:r 3727:4 3723:v 3717:= 3712:2 3707:| 3702:a 3698:| 3675:) 3670:) 3665:r 3661:t 3658:v 3652:( 3643:2 3635:+ 3631:) 3626:r 3622:t 3619:v 3613:( 3604:2 3595:( 3587:4 3583:r 3577:4 3573:v 3565:2 3561:r 3557:= 3552:2 3547:| 3542:a 3538:| 3512:4 3508:r 3502:4 3498:v 3491:) 3486:r 3482:t 3479:v 3473:( 3464:2 3454:2 3450:r 3446:+ 3439:4 3435:r 3429:4 3425:v 3418:) 3413:r 3409:t 3406:v 3400:( 3391:2 3381:2 3377:r 3373:= 3368:2 3363:| 3358:a 3354:| 3330:2 3325:| 3318:y 3314:a 3309:| 3305:+ 3300:2 3295:| 3288:x 3284:a 3279:| 3275:= 3270:2 3265:| 3260:a 3256:| 3225:2 3221:r 3215:2 3211:v 3204:) 3199:r 3195:t 3192:v 3186:( 3176:r 3170:= 3166:) 3161:r 3157:t 3154:v 3148:( 3138:r 3130:2 3126:t 3122:d 3116:2 3112:d 3106:= 3101:y 3097:a 3081:2 3077:r 3071:2 3067:v 3060:) 3055:r 3051:t 3048:v 3042:( 3032:r 3026:= 3022:) 3017:r 3013:t 3010:v 3004:( 2994:r 2986:2 2982:t 2978:d 2972:2 2968:d 2962:= 2957:x 2953:a 2928:y 2924:a 2901:x 2897:a 2872:) 2867:r 2863:t 2860:v 2854:( 2844:r 2841:= 2838:y 2826:) 2821:r 2817:t 2814:v 2808:( 2798:r 2795:= 2792:x 2760:2 2756:b 2751:= 2748:t 2721:) 2715:r 2709:2 2704:b 2701:v 2695:( 2685:r 2682:= 2679:y 2667:) 2661:r 2655:2 2650:b 2647:v 2641:( 2631:r 2628:= 2625:x 2599:0 2596:= 2593:y 2573:r 2570:= 2567:x 2542:v 2538:r 2532:2 2526:= 2523:b 2500:v 2480:r 2474:2 2451:) 2448:b 2445:( 2436:r 2433:= 2430:y 2419:) 2416:b 2413:( 2404:r 2401:= 2398:x 2375:b 2346:r 2340:2 2336:v 2332:m 2326:= 2323:F 2283:r 2277:2 2273:v 2269:m 2263:= 2260:F 2241:( 2211:( 2196:( 2180:( 2161:( 2146:( 2130:( 2113:( 2097:( 2062:( 2047:( 2027:( 2005:( 1983:( 1950:( 1930:( 1904:( 1877:( 1863:( 1833:( 1821:( 1795:s 1778:( 1753:( 1738:( 1720:( 1692:( 1686:) 1666:. 1643:r 1640:d 1636:t 1632:r 1617:( 1591:( 1585:B 1583:X 1581:v 1577:F 1550:( 1535:( 1476:( 1460:( 1402:( 1344:( 1163:. 1161:R 1156:R 1152:r 1150:( 1148:F 1136:, 1078:( 1004:c 999:F 961:T 958:2 955:= 950:c 945:F 936:r 910:r 906:T 903:2 897:= 892:c 888:F 861:c 857:F 853:r 847:T 844:2 836:2 832:v 828:m 802:c 798:F 777:T 743:T 740:2 737:= 732:c 727:F 718:r 617:( 575:c 532:( 301:( 251:. 195:F 191:r 187:F 183:r 179:a 172:a 168:F 127:( 110:( 84:( 50:.

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

Index