# Centrifugal vs. centripetal force? **URL:** \ **Category:** Factual Questions\ **Created:** [May 11, 2004, 7:30am UTC](https://boards.straightdope.com/t/centrifugal-vs-centripetal-force/244594 "2004-05-11T07:30:41Z")\ **Posts on this page:** 12\ **Page:** 2
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [May 12, 2004, 12:40am UTC](https://boards.straightdope.com/t/centrifugal-vs-centripetal-force/244594/21 "2004-05-12T00:40:18Z")
> [@dakravel](#): > > Not always, you’re trying to apply logic valid in non-accelerated frames into an accelerated frame. No such thing. The principle of general covariance says that it doesn’t matter. In fact, there’s no such thing as an “accelerated” or “non-accelerated” frame. It’s just that the curvature effects of the coordinate change are noticible for cases where we classically describe a “centrifugal” force. The percieved centrifugal force is just a side effect of the local diffeomorphism applied. ---
**Author:** ![Xema](https://avatars.discourse-cdn.com/v4/letter/x/9de053/32.png) [@Xema](https://boards.straightdope.com/u/Xema)\ **Post date:** [May 12, 2004, 1:13am UTC](https://boards.straightdope.com/t/centrifugal-vs-centripetal-force/244594/22 "2004-05-12T01:13:42Z")
> [@Ring](#): > > F = ma = mv[sup]2[/sup]/2 I don’t think this works. ma is certainly force, but mv[sup]2[/sup]/2 is energy (force time distance). ---
**Author:** ![robby](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/robby/32/11048_2.png) [@robby](https://boards.straightdope.com/u/robby)\ **Post date:** [May 12, 2004, 1:13am UTC](https://boards.straightdope.com/t/centrifugal-vs-centripetal-force/244594/23 "2004-05-12T01:13:50Z")
I think that the concept of centrifugal force just serves to help introductory physics students get even more confused about circular motion. People like **Chronos** and **scr4** can easily shift their thinking from an inertial reference frame to a non-inertial reference frame, but in my experience, your average student just gets them confused. I think that it’s best to consider only the inertial frame of reference, and keep centrifugal force out of the picture. (This is because, of course, centrifugal force does not exist in such a frame. And I’m not going anywhere near general relativity.) > [@Jinx](#): > > …don’t forces _always_ come in pairs??? 😕 > > Likewise, I, too, have never fully understood why we appear to be forced to lean away from the center (when in a car going around a curve) instead of being pulled inward. A friend once put it as your body wants to keep moving forward, but the car is turning and your body (still moving in a straight line - now always tangent to the curve) runs into the side of the car. Seemingly, it feels as if you have been pushed outwards. Is this how other SDopers have been taught to picture it? > > Even if this is a correct description, I fail to clearly see how one is under the influence of a center-seeking force. To this day, I have just come to accept it. The ball-on-a-rope example helps because I can picture the tension in the rope, but then another question comes to mind…there must be a reaction force to the tension in the rope, and hmm, would this reaction force actually be “pushing on a rope?” (Didn’t they teach us you don’t push on a rope?) - Jinx > [@Jinx](#): > > Wait a minute! Here’s another brain teaser! What about planets moving in an orbit? There’s no friction there, AND gravity pulls inward + centripetal force pulls inward, so why don’t the two forces add up as one big tug inwards? What keeps the planets in orbit? A-ha! You’d say centrifugal force, right? So, it is real, or not? Perhaps, it is an “observed” effect we mistakenly call a force? (But is that, more correctly, a reaction force???) By “forces always come in pairs,” **Jinx** , you are referring to Newton’s 3rd Law. What you have to realize, though, is that the pairs of forces **act on different objects.** To consider your various examples: 1. For a planet in orbit, the force pair is the attractive force of gravity of the Sun on the planet; and the attractive force of gravity of the planet on the Sun. The former is equivalent to the centripetal force on the planet. Note that the planet is undergoing circular motion, therefore it is accelerating, therefore by _F[sub]net[/sub] = ma_, there **is** a net force being exerted on it (the planet). The planet is being kept in orbit by this force. 2. For a ball on a rope, the force pair is the tension of the rope pulling the object in toward the center; and the tension of the rope pulling outward on your hand. Note that this outward force on your hand is **not** acting on the swinging object. 3. When you are in a car going around a curve, the force exerted on you by the car door is forcing you to go in the direction of the turn. The reaction force is the force exerted by you on the car door. Note that you can only feel that a force is being exerted on you; you cannot feel the direction of a force. The fact of the matter is that you are being forced inwards, despite your perception. 4. Another example is clothes in a washer during the spin cycle. The clothes are **not** being forced outward. Instead, the walls of the washer are exerting an inward force on the clothes that causes them to move in a circular path. ---
**Author:** ![robby](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/robby/32/11048_2.png) [@robby](https://boards.straightdope.com/u/robby)\ **Post date:** [May 12, 2004, 1:29am UTC](https://boards.straightdope.com/t/centrifugal-vs-centripetal-force/244594/24 "2004-05-12T01:29:01Z")
> [@Xema](#): > > I don’t think this works. ma is certainly force, but mv[sup]2[/sup]/2 is energy (force time distance). The equation is properly: _F[sub]net[/sub] = ma = F[sub]centripetal[/sub] = mv[sup]2[/sup]/r_, where _v_ is the tangential (linear) velocity, and _r_ is the radius of the circle in which the object is moving. ---
**Author:** ![dakravel](https://avatars.discourse-cdn.com/v4/letter/d/85e7bf/32.png) [@dakravel](https://boards.straightdope.com/u/dakravel)\ **Post date:** [May 12, 2004, 1:42am UTC](https://boards.straightdope.com/t/centrifugal-vs-centripetal-force/244594/25 "2004-05-12T01:42:17Z")
> [@](#): > > The previous comment was: Don’t forces come in pairs? Errr, I mispoke. My brain thought I was responding to one thing, when it wasn’t really that thing at all. I think the best way to think this from a physics student’s POV (i.e., no law of equivalence, no general relativity), is to constain a universe to just two objects. A single fencepost kinda thing and a ball connected to it by a string. No gravity, no nothing. You pull the string taut, and send the ball flying. Now the string is a carrier of force in a sense, so we’ll ignore the fact that the post is pulling on the string and the string is pulling on the ball and just say the post is pulling on the ball. So the post is pulling on the ball (centripetal force), but then there has be another second law force in there right? Well, the only other place force can come from is the ball pulling on the post. However, the post is more or less immobile, so it doesn’t move. That causes the ball to go around in the circle, only two forces, nothing called centrifugal force is needed. Of course in this situation, the forces will not all cancel, which seems to bother some. But that should be the case because the ball is constantly accelerating. ---
**Author:** ![Xema](https://avatars.discourse-cdn.com/v4/letter/x/9de053/32.png) [@Xema](https://boards.straightdope.com/u/Xema)\ **Post date:** [May 12, 2004, 1:45am UTC](https://boards.straightdope.com/t/centrifugal-vs-centripetal-force/244594/26 "2004-05-12T01:45:07Z")
[QUOTE=robby] The equation is properly: _F[sub]net[/sub] = ma = F[sub]centripetal[/sub] = mv[sup]2[/sup]/r_ [QUOTE] Right - that works. ---
**Author:** ![Ring](https://avatars.discourse-cdn.com/v4/letter/r/6a8cbe/32.png) [@Ring](https://boards.straightdope.com/u/Ring)\ **Post date:** [May 12, 2004, 2:11am UTC](https://boards.straightdope.com/t/centrifugal-vs-centripetal-force/244594/27 "2004-05-12T02:11:10Z")
> [@robby](#): > > The equation is properly: > _F[sub]net[/sub] = ma = F[sub]centripetal[/sub] = mv[sup]2[/sup]/r_, > > where _v_ is the tangential (linear) velocity, and _r_ is the radius of the circle in which the object is moving. Yeah, sorry for the typo. Of course if the radius just happened to be 2… ---
**Author:** ![Ring](https://avatars.discourse-cdn.com/v4/letter/r/6a8cbe/32.png) [@Ring](https://boards.straightdope.com/u/Ring)\ **Post date:** [May 12, 2004, 2:19am UTC](https://boards.straightdope.com/t/centrifugal-vs-centripetal-force/244594/28 "2004-05-12T02:19:52Z")
> [@AHunter3](#): > > Somewhere in there somehow is a concern about the velocity of very distant objects and a formula pertaining to radial velocity and linear velocity and radius and so forth, a thing that continues to make relativity smell more suspect when applied to rotational motion instead of linear motion…probably something that was explained in Physics the day I stayed home sick… From the physics faq [http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html#14](http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html#14) > [@](#): > > Stand up in a clear space and spin round. It is not too difficult to turn at one revolution each two seconds. Suppose the moon is on the horizon. How fast is it spinning round your head? It is about 385,000 km away so the answer is 1.21 million km/s, which is more than four times the speed of light! It sounds ridiculous to say that the moon is going round your head when really it is you who is turning, but according to general relativity all co-ordinate systems are equally valid including revolving ones. So isn’t the moon going faster than the speed of light? This is quite difficult to account for. > > What it comes down to, is the fact that velocities in different places cannot be directly compared in general relativity. Notice that the moon is not overtaking the light in its own locality. The velocity of the moon can only be compared to the velocity relative to other objects in its own local inertial frame. And of course no _information_ is propagating faster than light, which is really what relativity is all about. ---
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [May 13, 2004, 5:03pm UTC](https://boards.straightdope.com/t/centrifugal-vs-centripetal-force/244594/29 "2004-05-13T17:03:20Z")
> [@robby](#): > > I think that the concept of centrifugal force just serves to help introductory physics students get even more confused about circular motion. Very true. Perhaps it should never even be mentioned, but it is often the “easy explanation” offered in elementary schools. > [@](#): > > People like **Chronos** and **scr4** can easily shift their thinking from an inertial reference frame to a non-inertial reference frame, but in my experience, your average student just gets them confused. Frames of reference are hard to picture. It was a great help that scr4, I believe, helped define what one’s perspective would be as seen from each frame of reference. [quote] …By “forces always come in pairs,” **Jinx** , you are referring to Newton’s 3rd Law. What you have to realize, though, is that the pairs of forces **act on different objects.** To consider your various examples: 1. For a planet in orbit, the force pair is the attractive force of gravity of the Sun on the planet; and the attractive force of gravity of the planet on the Sun. The former is equivalent to the centripetal force on the planet. Note that the planet is undergoing circular motion, therefore it is accelerating, therefore by _F[sub]net[/sub] = ma_, there **is** a net force being exerted on it (the planet). The planet is being kept in orbit by this force. [quote] Although the above should seem so simple, I still do not _see_ it so clearly. Yes, I’ve run through the calculations, but it is a subtle concept to _see_. When someone says the sun tugs on the earth, and the earth tugs on the sun (mGM/R^2)…now, this very straight forward to me. And, while I understand why the tug from the sun can be equated to the centripetal force, it is not as obvious. The tug from the sun, it and of itself alone, is not centripetal force - for the sun tugs on me, too, for example. But, rather a coincidence of circumstance must be present for the centripetal force to manifest itself. I think my mental stigma is the way I was taught to picture things from way back. I shouldn’t just be thinking that gravity is pulling on a planet. Instead, I need to evaluate the whole superposition of circumstances to get the full picture. IOW, yes, gravity is pulling the planet inwards, but the planet has its own motion it would like to maintain (thank you very much) and its inertia will resist the inward pull hence combating the inward. Combining these two facts manifests the centripetal force. Well, at least it helps me to think of it like this now. Your other examples I have an easier time understanding and picturing. Thanks for your help, Robby…I say, olde chap, very good post! - Jinx ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [May 13, 2004, 5:44pm UTC](https://boards.straightdope.com/t/centrifugal-vs-centripetal-force/244594/30 "2004-05-13T17:44:58Z")
> [@Jinx](#): > > And, while I understand why the tug from the sun can be equated to the centripetal force, it is not as obvious. The tug from the sun, it and of itself alone, is not centripetal force - for the sun tugs on me, too, for example. But, rather a coincidence of circumstance must be present for the centripetal force to manifest itself. It sounds like you are thinking of centripetal force as a _consequence_ of rotation. It’s not. “Centripetal force” means “the force that is causing the object to move in a circular path.” If there was no force acting on an object, it will travel through space in a straight line. If a force pulls or pushes it sideways momentarily, it will “accelerate”, i.e. its path will be bent, and its velocity will change. (Speed will be the same, but velocity is a vector, and the direction of the vector will change.) If you can arrange a system so that a foce pushes or pulls an object to the side continuously, the object will accelerate continuously to the side; that is, its path will continue to bend. In other words, the path will be a circle. The force that is, um, forcing the object to stay in this path is the centripetal force. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [May 13, 2004, 8:57pm UTC](https://boards.straightdope.com/t/centrifugal-vs-centripetal-force/244594/31 "2004-05-13T20:57:30Z")
> [@](#): > > People like Chronos and scr4 can easily shift their thinking from an inertial reference frame to a non-inertial reference frame, but in my experience, your average student just gets them confused. > > I think that it’s best to consider only the inertial frame of reference, and keep centrifugal force out of the picture. (This is because, of course, centrifugal force does not exist in such a frame. And I’m not going anywhere near general relativity.) The problem with this is that students have actually experienced centrifugal force and are familiar with it. An introductory physics student might ask a question like “When the car turns quickly, why am I pulled towards the outside of the curve?”, but he’s not likely to ask “When the car turns quickly, why does the car door move in towards me?”. The question, as asked, is in the frame of reference fixed to the car, that is to say, the non-inertial frame, so it’s appropriate to answer it in the non-inertial frame. And **Jinx** , you should not consider “inertia” as a force. Depending on what you mean by “inertia”, it’d be a mass or a momentum, neither of which even has the same units as force. When a planet is in orbit, you can’t say that inertia is opposing the gravitational pull from the Sun. The only meaningful way to assign a direction to inertia would be the momentum, and that’s at a right angle to the gravitational force, not opposing it. You can say that the gravitational force is opposed by a centrifugal force, and that the planet is therefore not accelerating. Alternately, you can say that there’s nothing opposing the gravitational force (which, in this case, is the centripetal force), and that the planet is therefore accelerating. Why doesn’t the planet fall? The answer is, it does. An object in orbit is always falling. As for Newton’s laws not being valid in the rotating frame, they are, provided you introduce the fictitious forces, acting without a source. Which is, of course, why we introduce them in the first place. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [May 13, 2004, 9:59pm UTC](https://boards.straightdope.com/t/centrifugal-vs-centripetal-force/244594/32 "2004-05-13T21:59:32Z")
> [@Ring](#): > > And of course no _information_ is propagating faster than light, which is really what relativity is all about. Not really. Relativity is all about the principle of general covariance, which says that physics can’t depend on your reference frame at all. That no information propagates faster than light is a consequence of the hypothesis that spacetime is locally Lorentzian as well as the (philosophical) hypothesis of local causality. [Previous page](https://boards.straightdope.com/t/centrifugal-vs-centripetal-force/244594.md?page=1)