# What exactly is centrifugal force

by hms.tech
Tags: centrifugal, force
 P: 247 I think that there is no such thing as centrifugal force . Am I right ? is this force fictitious ?
 P: 5,462 For some systems that are not in equilibrium ie moving, D'Alembert introduced a method of applying a fictitious force to bring the system to equilibrium (rest). The equations of equilibrium could then be employed to solve the system. These equations then included the fictitious force. Centrifugal force is just such a force applied to objects executing circular motion.
 P: 247 What is the source of this force ? For example, in gravitational circular motion, where does this force originate from ?
P: 5,462

## What exactly is centrifugal force

It doesn't exist.
That is why it is fictitious.

However we can do the maths as though it did exist.
It is a mathematical trick.

The modern alternative is to use Newton's Laws of Motion, which I think came after D'Alembert, but I will check that.
 P: 49 If something as a source of centrifugal force exists, then I think it is the inertia.
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P: 6,764
 Quote by hms.tech I think that there is no such thing as centrifugal force. ... is this force fictitious ?
Depends on how you're using the term centrifucal force. There's the fictitious centrifugal force in a rotating frame. A less common (for physicists) usage is "reactive centrifugal force", which is part of a pair of Newton third law forces: say a string exerts a centripetal force on an object, then the object exerts a reactive outwards force on the string. Note that this "reactive centrifugal force" is not exerted on the object itself, but on the string. In a rotating frame, the fictitious forces, centripetal and coriolis (and euler if there is angular acceleration of the frame) all appear to act on the object. Wiki articles:

http://en.wikipedia.org/wiki/Reactive_centrifugal_force

http://en.wikipedia.org/wiki/Centrif...e_(fictitious)

http://en.wikipedia.org/wiki/Rotating_frame
P: 3,173
 Quote by Studiot It doesn't exist.
All forces are just mathematical models invented by humans.
 Quote by Studiot That is why it is fictitious.
"Fictitious force" is just an unfortunate name choice. It gives people the wrong idea that some forces are more "real" than others. But that is just philosophy, irrelevant to physics. That is why I prefer the terms "inertial forces" and "interaction forces".
P: 247
 Quote by A.T. All forces are just mathematical models invented by humans. "Fictitious force" is just an unfortunate name choice. It gives people the wrong idea that some forces are more "real" than others. But that is just philosophy, irrelevant to physics. That is why I prefer the terms "inertial forces" and "interaction forces".
Yes, I read this word "inertial" a lot on the Wikipedia link provided by rcgldr.

Can you explain this notion ?
 P: 5,462 hms.tech Before you get confusing explanations as to the different ways of regards motion under a central force or circular motion perhaps you would tell us what your course says ie which approach they take. Your exams will be based on this.
P: 247
 Quote by Studiot hms.tech Before you get confusing explanations as to the different ways of regards motion under a central force or circular motion perhaps you would tell us what your course says ie which approach they take. Your exams will be based on this.
Centripetal and centrifugal forces

I couldn't find the term centrifugal force in any of my physics books, hence I checked out PF. Can you provide some links (non Wikipedia) about centrifugal force .

I think this term was self created by humans for their own better understanding of the "motion" of objects in circular orbit.
We, the modern physicists would call it nothing but a consequence of the fact that any object undergoing circular motion tends to move in a straight line (tangential to its path) . So it can be thought of as "inertia" , but I would stick to my claim that this force is non existent.
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P: 6,764
 Quote by hms.tech Yes, I read this word "inertial" a lot on the Wikipedia link provided by rcgldr. Can you explain this notion ?
An "inertial" frame of reference means the frame of reference is not accelerating (no linear acceleration and no rotation). Newton's laws of physics apply in an inertial frame without any modification.

If the frame was accelerating, such as a rocket in space, then to an observer inside the rocket, there would be an apparent force on any object within the spacecraft, similar to gravity on earth.

The wiki article on this goes into more detail:

http://en.wikipedia.org/wiki/Inertia...e_of_reference

 Quote by hms.tech I couldn't find the term centrifugal force in any of my physics books, hence I checked out PF. Can you provide some links (non Wikipedia) about centrifugal force.

 Quote by hms.tech So it can be thought of as "inertia" , but I would stick to my claim that this force is non existent.
In your diagram of the car in a turn, there is a Newton third law pair of forces, an inwards centripetal force exerted by the road onto the car, and an equal in magnitude but opposing outwards reaction force that the car applies to the road. That outwards force is real, the issue for some people is using the term "reactive centrifugal force" to describe that outwards force that the car exerts to the road.
 P: 5 A more simple example might serve to make this clear: consider a train that is accelerating with acceleration a. You are on this train and you drop a ball. The only force due to a physical interaction acting on the ball is that of gravity which is due to the ball's interaction with the Earth. However, you see the ball accelerating away from you with the same magnitude of acceleration as that of the acceleration of the train. Thus if we consider the acceleration of your reference frame (keep in mind that since you're measuring the motion of the ball with your position as the origin, you are at rest in your reference frame) as the source of a force on the ball, it applies a force of magnitude ma, where m is the mass of the ball. This force isn't due to any physical interaction that you can observe, that's why we call it fictitious. I agree that calling it fictitious is confusing and that inertial is less confusing and also an apt name in that the magnitude of the force is proportional to the mass of the object A similar thing happens when you're in a rotating reference frame (for instance say someone does this while on a merry go round) except that now this fictitious force is directed outwards from the center of the merry go round. This type of fictious force due to being on an accelerated (or noninertial reference frame) is called centrifugal. A centripetal force is the net force in the radial direction due to real forces and is generally talked about in an inertial or non-accelerated reference frame. Hope that clears it up a bit
 P: 5,462 Look at post#9 of this thread. http://www.physicsforums.com/showthr...trifugal+force It puts what I said in post#2 here into equations.
P: 3,173
 Quote by hms.tech Yes, I read this word "inertial" a lot on the Wikipedia link provided by rcgldr. Can you explain this notion ?
http://en.wikipedia.org/wiki/Fictitious_force

In short: Newton based his laws of motion for inertial reference frames on interaction forces. To generalize some of the laws so they apply to non-inertial frames inertial forces were introduced.
 P: 5,462 Gosh I'm glad I didn't meet that wiki as my first introduction to centrifugal force. It's one saving grace is that at the very bottom it refers to the D'alembert's principle of inertia wiki. That is much more digestible. http://en.wikipedia.org/wiki/D%27Alembert%27s_principle Look towards the end of the much shorter page.
 P: 1,397 Here's a mathematical way to think about fictitious forces. Suppose you have a velocity vector $\stackrel{\rightarrow}{U}$ which is constant (no forces acting on it). That means $\dfrac{d}{dt}\stackrel{\rightarrow}{U} = 0$ Now, this is a vector equation. It's common for people to denote vectors by ordered pairs: $\stackrel{\rightarrow}{U} = (U^x, U^y)$, where $U^x = \dfrac{dx}{dt}$ and $U^y = \dfrac{dy}{dt}$. But that's actually a BAD notation, because what it really means to write a vector as components is that we've chosen certain vectors called basis vectors, and we've expressed $\stackrel{\rightarrow}{U}$ as a combination of those basis vectors. So a better way to write it is $\stackrel{\rightarrow}{U} = U^x\ \hat{e_x} + U^y\ \hat{e_y}$ When you write it this way, you can see that $\dfrac{d}{dt}\stackrel{\rightarrow}{U} = \dfrac{dU^x}{dt} \hat{e_x} + U^x \dfrac{d \hat{e_x}}{dt} + \dfrac{dU^y}{dt} \hat{e_y} + U^y \dfrac{d \hat{e_y}}{dt}$ Of course, the most important fact about Cartesian coordinates is that the basis vectors are constant. So the terms $\dfrac{d\hat{e_x}}{dt}$ and $\dfrac{d\hat{e_y}}{dt}$ are both zero. But if you switch to polar coordinates $r,\theta$, it's no longer the case that the basis vectors are constant. So you get additional terms having to do with the rate of change of the basis vectors. Those additional terms are the "fictitious forces". I'm going to spare the details, but it turns out to be, in polar coordinates: $\dfrac{d}{dt}\stackrel{\rightarrow}{U} = (\dfrac{dU^r}{dt} - r (U^\theta)^2) \hat{e_r} + (\dfrac{dU^\theta}{dt} + \dfrac{2}{r} U^r U^\theta) \hat{e_\theta}$ where $U^r = \dfrac{dr}{dt}$ and $U^\theta = \dfrac{d \theta}{dt}$. So, if there are no forces acting on an object, then $\stackrel{\rightarrow}{U}$ will be constant, but that doesn't mean the components will be constant. Instead, the components will obey: $\dfrac{dU^r}{dt} = r (U^\theta)^2$ $\dfrac{dU^\theta}{dt} = - \dfrac{2}{r} U^r U^\theta$ So it seems that there are "fictitious" forces acting on the object, causing the components of the velocity to change. Nonconstant basis vectors give rise to nonconstant components of velocity, even in the absence of any real forces.
P: 247
 Quote by rcgldr In your diagram of the car in a turn, there is a Newton third law pair of forces, an inwards centripetal force exerted by the road onto the car, and an equal in magnitude but opposing outwards reaction force that the car applies to the road. That outwards force is real, the issue for some people is using the term "reactive centrifugal force" to describe that outwards force that the car exerts to the road.
If you think about it, the reactive force is just the force exerted by the car on to the road, but this does not relate (even remotely) to the diagram .
The diagram shows that there "seems" to be a force acting on the objects which tend to move outward (in the opposite direction of centripetal force). So the force you talked about is the force exerted by the car on the road and not the objects.

You are sitting on the backseat of a car, and this car is turning around a corner at high speed. You would have noticed yourself moving outwards (right ?) until you reach the door of the car which then would provide the appropriate centripetal force to your body.
Notice that this situation is based on the fact that friction could not provide the centripetal force. Notice also that at all times you would be "FEELING" some outward push , (again , which in my opinion is just inertia but not centrifugal force)

Am I right in the above mentioned aspect ?
P: 3,173
 Quote by hms.tech Am I right in the above mentioned aspect ?
You switch frames back and forth and confuse the issue. Stick to an inertial frame, and there are no inertial forces. Stick to a non-inertial frame, and you always have inertial forces which act just like interaction forces (except Newtons 3rd).

Both is correct and leads to the same quantitative predictions, which is all that matters in physics. Musings about "realness of forces" is philosophy.

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