Centrifugal Force Query

[tronton_]

Just a simple question, use as much detail as you like in answering it.

I'm a high-school Physics student, and my Physics teacher said Centrifugal Force doesn't actually exist. After being a long time reader of xkcd, I've seen Centrifugal Force mentioned a couple of times. So, I thought I'd research it, mostly I've found sources saying it doesn't exist, but I've also found that it is measurable with a formula. So, I'm not 100% sure about it, can someone please explain it to me?

[Moose Hole]

I think it has something to do with inertial reference frames. Pretty much if the reference frame is rotating, then something outside the reference frame is rotating it. That outside thing is providing a centripetal force which is observable in its reference frame, but observed differently within the rotating reference frame. At this point I get confused so I'll stop.

[Aiwendil]

Centrifugal force is a "fictitious force". If you have something rotating and you analyze it from the point of view of a stationary observer, then there is no centrifugal force. In other words, in this case, the motion of everything is correctly described using the real forces that apply. For example, suppose you're standing still and swinging a bucket full of water in a circle. If you were to use Newton's law F = ma, with F being the sum of the force of gravity and the force you're exerting on the bucket, this would correctly describe the motion of the of the water in the bucket. In this case, there is no centrifugal force. Incidentally, the force that you are applying to keep the bucket moving in a circle is called the centripetal force.

However, suppose you wanted to calculate things from the point of view of an insect trapped inside the bucket, from whose point of view the bucket is stationary. This switch - from considering yourself stationary and the bucket moving to considering the bucket stationary and the stuff outside of it moving - is called a change in the "frame of reference". In particular, you are switching to a rotating frame, which is a type of "non-inertial frame". When you switch to a non-inertial frame, you have to add fictitious forces. In the case of a rotating frame, you must add two additional forces in order for F = ma to work correctly. These are the coriolis force and the centrifugal force. In other words, if you try to calculate the motion of the water in the rotating frame using just the same old forces you used in the stationary frame, you will get the wrong answer. To get the correct answer, you have to include centrifugal and coriolis terms.

[idobox]

Very good explanation Aiwendil.

I would like to add a small image.
Imagine you tie a mass at the end of a rope, and make it turn.
In your reference frame, there is only one force applied on the mass, the tension, toward the center (centripetal). So the mass always accelerate toward the center, and since its speed is tagential, it gives a circular trajectory.
In the mass reference frame, the mass obviously doesn't move. Its acceleration must be null, so you need a force that compensate the tension of the rope, a centrifugal force.

This centrifugal force, is like the force you feel when a car is accelerating or braking. It might look like a mathematical trick, but it can break your bones in real life.

[KittenKaboodle]

What ?, nobody gave a link to: "No, Mr Bond, I expect you to die." http://xkcd.com/123/

[Solt]

You guys really suck at explaining fictitious forces. You shouldn't ever use the term "rotating reference frame" unless you can actually draw a rotating reference frame. It's a mathematical term, and should be described using math. Simply knowing the name doesn't even start to describe how these other forces come about.

The exact nature of the centrifugal force is actually hard to describe qualitatively. So let me describe how the other fictitious force, the coriolis force, works since it is far more intuitive.

Say you are on a plane that wants to fly in a perfectly straight line from north to south (we are in the northern hemisphere). Say it is using some sort of on-board guidance system to accomplish this, such as an inertial navigation unit, that can tell you if you are flying straight without need for any external reference such as stars or ground radar. Say also that there is no crosswind that day. Say that you take off and use GPS to point exactly at your destination, then turn the GPS off and rely entirely on your instruments for the rest of your flight.

If you attempt the flight, and if your on-board instruments say you have flown in a straight line, you will arrive at your destination and find that you have missed it by several dozen to several hundred miles to the west. That is to say, the destination is significantly east of where you expected it to be. What happened? Well, it's obvious that the earth turned below you while you were in the air. But if you didn't know that, and you knew your instruments were perfect, you would think that some mysterious force has "pushed" you many miles westward. This is known as the coriolis force, and that's exactly how it works- when something is spinning and something else is moving in a straight line nearby but not on the surface, and when you choose a reference point on the surface, to the person not on the spinning object it looks like there is a mysterious force pushing them in the opposite direction to the spin. But really, the object is spinning below them and they are being left behind. You can intuitively tell there is nothing strange going on here, but to a guy in a very small plane next to a very huge earth, it doesn't quite look so simple.

The Coriolis force is just an expression of the Newton's laws of motion that you already know- an object in motion will stay in motion unless acted on by an outside force. In this case there is nothing causing the plane to move in a circle, so it will not move with the earth in that direction but rather stay on its own path. If you formulate the equations of motion correctly (ie, taking into account the fact that one object is spinning and the other is not and that there is some relative motion between the two), they will account for this with an extra mathematical term. The term has no physical meaning other than what I've described above, it is purely bookkeeping to make sure that the final answer is correct. That's where the terms "rotating reference frame" and "fictitious force" come from.

The centrifugal force is quite similar, and only comes into play when you get a significant amount of initial velocity because you jumped off (or are touching) a spinning object. I'm not going to describe it because this post is getting pretty long already and it requires a tiny bit of math, but needless to say it's just Newton's law of inertia in action again. It's also a lot cooler than Coriolis in certain situations. Let me know if you want an explanation similar to how I explained the Coriolis force.


Edit: I think I need a disclaimer. What I have described is actually the Coriolis effect, which is the integral of the Coriolis force. A force is an acceleration and an acceleration is the change in velocity. So actually the Coriolis force would say that as the airplane ascends, the rate of this sideways shift as a result of the earth rotating gets worse. When the plane stops ascending, the effect settles on a constant value, at which point the Coriolis acceleration is zero but the "Coriolis velocity" is constant and nonzero. It all describes the same phenomenon though, which is a consequence of rotating observers and all that jazz. The distinction between force and effect just adds needless complexity, so you can probably ignore it unless you are trying to design rockets or something.

[p1t1o]

As far as I am concerned, unless the context is quite specifically inappropriate, then centrifugal force can be considered to act as per its layman's description.

Aslo, this.

[SlyReaper]

You guys really suck at explaining fictitious forces.

<terrible long-winded explanation of fictitious forces which confuses everything>

No, I think they had it pretty much bang on. A rotating reference frame is not a hard thing to explain or visualise without resorting to deep maths. A reference frame is just a point of view; a rotating reference frame is just the point of view of something rotating. As mentioned above, you experience it every time you turn a corner in a car.

[tronton_]

You guys really suck at explaining fictitious forces...

Thanks, this was really helpful. I actually get it now, and thanks everyone else. This has helped a lot. I think I understand it now, which is good.

Thanks again guys.

[Solt]

A rotating reference frame is not a hard thing to explain or visualise without resorting to deep maths.

Of course not, but it tells you nothing about how the centrifugal force or coriolis force actually arises unless you use "deep maths" (it's just vector algebra). It's not the frame that is important to understanding these forces, it's the motion of the body that causes them.

<terrible long-winded explanation of fictitious forces which confuses everything>

I take offense at this. Did you even read my explanation? It was very, very clear and explains exactly the nature of the coriolis force. In what kind of world does someone get away with accusing a better explanation of "confusing everything"? What kind of explanation is "fictitious forces are the forces you have to add to make F=ma work correctly in a rotating reference frame"? That means NOTHING. He didn't even explain what he meant by F=ma not working. He didn't explain what's so special about a rotating reference frame that causes it to not work. To a high school student who probably has never heard of integration, that means nothing.

Sorry, but if you think Aiwendil's explanation was better than mine, you are exemplifying everything that is wrong with science education. Throwing around extremely abstract math concepts like "the equations won't work in a rotating frame!" is NOT explaining anything. The only reason science education doesn't fail as is is because bright students take an explanation like that and spend hours deconstructing it until they get an intuitive understanding. And then they feel so good about themselves because they know the meaning of these mystical terms, and they explain it to the next guy in the same crappy way, self confident that they are using precise language and everything they need to figure it out is in the statement. It's nothing but masturbation.

a rotating reference frame is just the point of view of something rotating. As mentioned above, you experience it every time you turn a corner in a car.

I'm not sure you understand it yourself. A rotating reference frame is not something "you experience every time you turn a corner in a car." There's no one standing there with a pair of coordinate axes pointed on you as you spin around them. The frame means nothing, it's a convenient mathematical tool to keep you organized when you are trying to keep track of complex relative motion. Just because a rotating reference frame is used, does not mean you will feel real centrifugal force. The two concepts are only related in special cases (for an example of a rotating reference frame where centrifugal force arises but you don't feel anything like you do in a car, check out this wikipedia example: http://en.wikipedia.org/wiki/Centrifuga ... pping_ball). The idea of a rotating reference frame is NOT a substitute (or an explanation) for what is actually going on, which is that inertia is causing you to move in a different direction than the now rotating body.

[Aiwendil]

Sorry, but if you think Aiwendil's explanation was better than mine, you are exemplifying everything that is wrong with science education. Throwing around extremely abstract math concepts like "the equations won't work in a rotating frame!" is NOT explaining anything.

Look, I wasn't trying to write a mechanics text book or anything. The guy was just wondering why he'd heard centrifugal force described as 'not a real force' sometimes, and I decided to take a couple minutes before leaving for work in the morning and try and explain it to him.

For what it's worth, I found your explanation adequate in itself. But whatever respect that may have earned you from me (and, I feel confident in asserting, from other posters on this board) was wiped away and then some by your utter lack of civility. Please, learn some manners before embarking on your crusade to improve the quality of physics education. Also, you might want to focus on actual physics teachers rather than would-be helpful forum users.

[SU3SU2U1]

To avoid confusing things, its best to think of linear motion first. And no, you won't need any mathematics.

You know how when you slam on the gas in a car, you feel like you are being pushed into the seat? That is a 'fictitious force.' Someone standing outside the car will say "aha! The car is actually accelerating towards you/pushing you forward! You are accelerating!" In some sense, its not a 'real' force, its a consequence of thinking of the car as your 'frame of reference'. Similarly, when you are in one of those spinning carnival rides, you feel like you are being pushed into the wall. Thats the centrifugal force.

Side note- these forces are as fictitious as gravity, which you can also make go away by a suitable choice of reference.

[Nlelith]

<terrible long-winded explanation of fictitious forces which confuses everything>

I take offense at this.

Pay him no mind, I thought your explanation was wonderfully intuitive. I actually feel ashamed for not knowing that this is how the coriolis force arises. I'd be very much interested in your explanation of the centrifugal force.

[SlyReaper]

<terrible long-winded explanation of fictitious forces which confuses everything>

I take offense at this.

I took offense at "you guys really suck at explaining". Guess we're even. I thought you talking about the coriolis force would just confuse matters because the OP had not asked about the coriolis force, but judging by subsequent posts here, I was mistaken. I apologise for that.

I still think my "car turning a corner" example was sound. You don't need axes, you just need reference points which are fixed within the rotating frame. The dashboard lights or the hems on the seat fabric serve just as well as a set of axes, unless you really do want to do the proper maths. The OP seemed to be asking for an intuitive explanation, not necessarily a mathematical one.

[Qaanol]

Gravity is also a fictitious force. When you stand up, the “real” force on you (caused by exchange of virtual particles) is electromagnetic repulsion from the ground pushing you up. Without that force, you would follow a natural geodesic path through spacetime, and it is only the continued application of the normal force that keeps you out of a geodesic. However, when viewed from the reference frame of someone standing on the ground, it feels like there is a gravitational force “pulling” you down.

You can develop a valid theory of motion by treating gravity as a force. This is common in Newtonian dynamics, and is what most people are taught in a first physics course. Similarly, you can develop a valid theory of motion treating centrifugal forces as real. For example, standing on the rotating earth you weigh less than you would if the earth were not rotating. You can think of this as a centrifugal force partly counteracting the force of gravity, which is a description in terms of two fictitious forces. Or you can think of it entirely in terms of real forces, in which case the real force needed to keep you out of the geodesic on the rotating earth is less than it would be on a still earth, because the geodesic path of your motion is now partly to the side, not straight into the earth.

[Solt]

In the strictest mathematical sense, centrifugal force is a misnomer. Imagine we are standing on the earth, which is rotating (but we don't know that), and the moon is actually stationary in space (neglect gravity, say the moon is actually just a point in space). To us it will look like the moon is rotating around us. Of course we know that in circular motion, you must always have a constant inward force to keep the object in a circle, otherwise it would go flying away. In this case, a centripetal force term arises that plays that role, analogous to gravity in the real earth-moon system. [resisting urge to use math]. This term is necessary because otherwise the things we know about circular motion (namely that you need a force to keep it in a circle) wouldn't make sense to someone on the rotating earth- to them, it would look like it's being kept there by magic!

Just like we constructed a situation in which a fictitious centripetal force arises, we can construct a situation in which a fictitious centrifugal force arises. First let's review a basic fact about circular motion: as an object moves around in a circle, at any instant if you "freeze" the system and look at the direction in which the object is actually moving, its velocity is tangent to the circle. There is always some central force, and this force is constantly "turning" the object so that it does not continue in that tangent direction but rather stays in the circle. But if this force (such as a string) were suddenly cut, the object would continue along the tangent instead of continuing to move in a circle.

Knowing that, say we have a spinning tire-like space station in an otherwise empty universe. Say there is a person hanging on to the outside of the station, who lets go of a ball. The ball shoots out away from the station on a path tangent to where it was released. Now to us, viewing everything from a stationary point outside of the station, we are simply seeing the natural consequence of circular motion- the ball moves off in a straight line. Nothing weird about that. But what does the astronaut, who doesn't know the station is rotating, see? Well, he lets go of a ball and it flies outward from the point of release and curves to the side - centrifugal and coriolis forces. So once again, we see that these fictitious forces are simply ways of describing to a rotating observer things that are perfectly obvious to the stationary observer.

What does this have to do with a car in a turn? Well, just imagine that instead of releasing the ball on the outside of the station, the astronaut releases it on the interior by reaching towards the center of the station before letting go. Once again the ball immediately starts moving in a straight line from its point of release, but a few seconds later it crashes back into the interior walls of the station. The key word is "crashes" - because the ball was actually moving in a different direction (though not necessarily at a different speed) than the rotating station walls. This is exactly the force you feel when you execute a turn in a car. The car itself is now following the curve of a circle of some radius, but because you are not connected to the car very firmly, you were essentially "let go" when the car started to make the turn. So you move in a shorter straight line, while the car turns, and you "crash" back into the side. This is obviously a huge exaggeration of the movement, because it actually happens in one smooth, continuous motion. But still, I said "straight line" and that is at odds with the fact that you are thrown sideways as the car turns, not forward. If that's bothering you, this last little bit should clear things up.

Let's return to the interior of the space station. You've heard those proposals about using spinning space stations to simulate gravity, right? Well that's centrifugal force in action. It would really create "gravity" because it is a force that pushes things outward. But all of the explanations I've given have said that things only move in straight lines unless they are connected to the station, so how does that make sense? This is very hard to explain without drawing, but I'll try (might want to draw it out yourself... think of what things would look like from the perspective of the astronaut). Let's return to the astronaut releasing a ball on the interior of a spinning space station, except this time remember to keep track of where the astronaut is as the ball moves. We know that at the point of release, the astronaut and ball are moving at the same speed, but the ball takes a straight line path until it crashes back into the walls while the astronaut follows the curved path of the station walls. But really, if the station is large enough, the straight line path of the ball is pretty much the same distance as the curved path of the station wall. So both the ball and the astronaut start at the same speed, and travel the same distance... the ball stays right next to the astronaut the whole time! If he outstretches his arm and lets go of the ball, when it crashes into the wall of the station, the astronaut will be there waiting. It will be just like if you dropped a ball on earth and it hit the ground next to your feet. If the astronaut gives the ball a light toss towards the center of the station, it will again move in a straight line as the astronaut spins around the outside and eventually he is nearby at the point and time when the balls touches the wall again. What does that remind you of? Gravity! To the astronaut, the straight line motion will look almost exactly like gravity! How does this explain why you are thrown outwards in a turning car? Well, on the station the apparent acceleration is between the ball and the side of the station. If you took a ride on the ball it would look like you were being pushed away from the center of the station, towards the outer wall. So the relative acceleration is outward, even though in the stationary frame you are moving in a straight line. In the car, the body of the car is the space station and you are the ball, so you feel like you are being pushed out from the center of rotation, which is why you get thrown sideways relative to the car. In the big picture however, you are still moving (or at least trying to move) in a straight line.

There's one other interesting consequence if you think about the spinning space station. If the space station is relatively small compared to the humans inside, the approximation I made earlier about how the straight line path of the ball is about the same distance as the curved path of the astronaut isn't very accurate. In this case, the straight line is dramatically shorter, but initial velocity of both the ball and astronaut is the same upon release. What does this mean? Mainly that the ball will never land back where the astronaut is standing, it will always land "ahead" of him. If you throw the ball hard enough straight up, you will never be able to catch it again without moving! Or, you would have to throw it "behind" you (opposite to the direction in which the station is rotating) in order to slow it down a bit, in which case you'd be able to catch it (if you got the speed and angle exactly right). Because of these strange effects, centrifugal force is not an accurate simulation of gravity! If you don't see what I mean let me know and I can find or draw pictures to show what I'm trying to say in words.

As a final note, you should be able to see now why centrifugal force is fictitious even though it causes very real effects. These effects are real and exist because you are touching a spinning body, and basically being thrown off of it, in a tangent line. To a stationary observer, no extra forces are needed to explain these motions, the traditional F=ma and knowledge of the conditions of central force circular motion are sufficient. But for someone who doesn't know he is on a spinning body, you would have to introduce extra force terms to make the motions they observe make sense. Otherwise they would see earth-like gravity occur on a space station with negligible mass and flip a shit.

[Hatter]

For example, standing on the rotating earth you weigh less than you would if the earth were not rotating.

So you weigh less on the poles? Or is this counteracted by the earth bulging in the middle, leaving you closer to the centre of the earth at the poles, increasing weight?
Also your post was actually really useful. Thanks.

I have one other question which has been bugging me. If I were sitting on a rotation platform, the objects I see would appear to be rotating the other way, so from my reference frame, everything else is rotating, but it does not seem to experience these forces. Can anyone explain this to me?

[Solt]

So you weigh less on the poles?

You would weigh more since they are not spinning. Centrifugal force is greatest 90 degrees from the axis of rotation.

If I were sitting on a rotation platform, the objects I see would appear to be rotating the other way, so from my reference frame, everything else is rotating, but it does not seem to experience these forces. Can anyone explain this to me?

Read the first paragraph of my last post. You are right, the objects you see are not actually experiencing those forces. So if you tried to explain the motion you saw with F=ma it would not work (there is no F!... not from gravity, not from a string, not from any phenomena that you will ever be able to detect). This is how fictitious forces arise; if you formulate the equations of motion to transform observations in a stationary frame to accelerations in a rotating frame, a centripetal force term would arise, which will account for the fact that the object is in circular motion (playing the role of gravity, for example). The force does not actually exist, but if you solve the equations for someone on a rotating platform they will describe the observed circular motion correctly. It is purely bookkeeping. Now, if you did not know you were spinning you would be very lost, since you would think it's a real force!

[Soralin]

Specifically: http://en.wikipedia.org/wiki/Gravity_of_Earth

In combination, the equatorial bulge and the effects of centrifugal force mean that sea-level gravitational acceleration increases from about 9.780 m·s⁻² at the equator to about 9.832 m·s⁻² at the poles, so an object will weigh about 0.5% more at the poles than at the equator.[3] [4]