# Textbook says there's no such thing as a centrilfugal force

## Homework Statement

what about the reaction force to a ball swinging in circles on a string or a rollercoaster doing a loop.

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Simon Bridge
Homework Helper
You need an unbalanced force to get an acceleration.

In the ball-on-a-string example, the ball pulls on the string only in the reference frame of the ball ... i.e. non-inertial. Relative to the person holding the string - they are pulling on the string, and, therefore, the ball. The pull is an unbalanced force pointing to the center, causing the acceleration.

The centrifugal "force" is an effect that comes from an accelerating reference frame.
We call these "pseudo-forces".

An easier example of a pseudoforce is when you are in an enclosed box (inside a cargo container maybe) which has a light-fitting (so you can see) suspended from the ceiling. You notice that the light hangs at an angle to the ceiling ... the mysterious force holding it at the angle is a pseudoforce, what's happening is that the box you are in is accelerating.

You need an unbalanced force to get an acceleration.

In the ball-on-a-string example, the ball pulls on the string only in the reference frame of the ball ... i.e. non-inertial. Relative to the person holding the string - they are pulling on the string, and, therefore, the ball. The pull is an unbalanced force pointing to the center, causing the acceleration.

The centrifugal "force" is an effect that comes from an accelerating reference frame.
We call these "pseudo-forces".

An easier example of a pseudoforce is when you are in an enclosed box (inside a cargo container maybe) which has a light-fitting (so you can see) suspended from the ceiling. You notice that the light hangs at an angle to the ceiling ... the mysterious force holding it at the angle is a pseudoforce, what's happening is that the box you are in is accelerating.
But my textbook also says that Newton's 3rd law implies that object A's force on object B will be equal and opposite to object B's force on object A. So I still don't understand how there can be an unbalanced force if Newton's 3rd law holds.

jtbell
Mentor
To clarify our rules: conceptual questions like this are OK in the "regular" forums. The "homework" forums are for getting help with specific exercises (for homework or otherwise).

I've moved this to "General Physics" in the main section.

Simon Bridge
Homework Helper
But my textbook also says that Newton's 3rd law implies that object A's force on object B will be equal and opposite to object B's force on object A. So I still don't understand how there can be an unbalanced force if Newton's 3rd law holds.
Newton's third law does not balance forces.

eg. gravity pulls down on you as you sit in your chair.
The reaction force to this acts at the center of the Earth and pulls the Earth upwards towards you.

There is also a force from the chair that stops you from falling. You press equally hard on the chair.

Remove the chair and the gravity force is said to be "unbalanced" - you accelerate towards the earth and the Earth accelerates towards you.

To have an acceleration, the forces must be unbalanced in this way.
In circular motion, there must be an acceleration since the velocity changes direction.
This follows from the definitions of velocity and acceleration as vectors.

The instantaneous direction of the change in velocity is towards the center.
Hence there is an unbalanced force acting towards the center.

Assuming that centrifugal force is a real force the way Newton defined them:
For the ball on the string, the tension in the string, the weight of the ball, and the centrifugal force, sum to zero. This means the ball is not accelerating. But we know it is accelerating because we can see its velocity is changing. This is a contradiction - so we discard the assumption.

The effect is real - it is just unhelpful for you to think of it as a force.

ehild
Homework Helper
But my textbook also says that Newton's 3rd law implies that object A's force on object B will be equal and opposite to object B's force on object A. So I still don't understand how there can be an unbalanced force if Newton's 3rd law holds.
You can not add forces which act on different bodies. The forces acting on the same body will add up. B exerts force F on A, if there are no other forces acting on A, the object A will accelerate with a=F/mA. A exerts force on B and and causes B to accelerate.

The swinging ball feels the pull of the string, the tension in the string. The ball pulls the string, so the string feels the reaction force of its pull.
In a roller-coaster, the normal forces and gravity keep bodies moving together with the roller-coaster in a loop. For people in the roller coaster, it is a rotating frame of reference, you feel the centrifugal force pointing outward, balanced by the normal force/gravity.

ehild

The swinging ball feels the pull of the string, the tension in the string. The ball pulls the string, so the string feels the reaction force of its pull.

ehild
Isn't the ball's pull a force in the opposite direction from towards the center?

Newton's third law does not balance forces.

eg. gravity pulls down on you as you sit in your chair.
The reaction force to this acts at the center of the Earth and pulls the Earth upwards towards you.

There is also a force from the chair that stops you from falling. You press equally hard on the chair.

Remove the chair and the gravity force is said to be "unbalanced" - you accelerate towards the earth and the Earth accelerates towards you.

To have an acceleration, the forces must be unbalanced in this way.
In circular motion, there must be an acceleration since the velocity changes direction.
This follows from the definitions of velocity and acceleration as vectors.

The instantaneous direction of the change in velocity is towards the center.
Hence there is an unbalanced force acting towards the center.

Assuming that centrifugal force is a real force the way Newton defined them:
For the ball on the string, the tension in the string, the weight of the ball, and the centrifugal force, sum to zero. This means the ball is not accelerating. But we know it is accelerating because we can see its velocity is changing. This is a contradiction - so we discard the assumption.

The effect is real - it is just unhelpful for you to think of it as a force.
I definitely see your side - the correct side. But I just can't get the reaction force out of my head, 'where there's a force, there's an equal and opposite reacting force'.

There is something else odd about all of this. My grade 12 physics notes and textbook talks a lot about centripetal force. But my university physics textbook only ever mentions a(rad), never once mentions "centripetal force".

A.T.
But my textbook also says that Newton's 3rd law implies that object A's force on object B will be equal and opposite to object B's force on object A. So I still don't understand how there can be an unbalanced force if Newton's 3rd law holds.
Yes, there is a 3rd Law reaction force (acting on object B) to the centripetal force (acting on object A). This reaction force is sometimes called "centrifugal", because it acts outwards (depending on how you define your objects). This force is a "real" interaction force and exists in every reference frame:
http://en.wikipedia.org/wiki/Reactive_centrifugal_force

But what your text book probably means by "not existent" is the inertial (fictitious, pseudo) centrifugal force that appears only in rotating reference frames. This is not a "real" interaction force, bust just a artifact of the non-inertial coordinate system. It doesn't obey Newtons 3rd Law. But otherwise it can be treated mathematically as a force when working in rotating coordinate systems:
http://en.wikipedia.org/wiki/Centrifugal_force_(rotating_reference_frame)

Keep those two distinct meanings in mind to avoid confusion. Unfortunately some book authors are terribly confused themselves and conflate the two.

BruceW
Homework Helper
Isn't the ball's pull a force in the opposite direction from towards the center?
yes, but this force is acting on the string.

edit: And this is the reason why the string goes horizontal. (otherwise, it would just point down towards the floor).

Yes, there is a 3rd Law reaction force (acting on object B) to the centripetal force (acting on object A). This reaction force is sometimes called "centrifugal", because it acts outwards (depending on how you define your objects). This force is a "real" interaction force and exists in every reference frame:
http://en.wikipedia.org/wiki/Reactive_centrifugal_force
So there really is a centrifugal force. Maybe the misunderstanding that people have, including my grade 12 physics teacher, is that the centrifugal force does not exist on its own, contrary to what experiments show, like the glass of water that morphs the same way to rotating acceleration or linear acceleration.

A.T.
So there really is a centrifugal force.
There is a "real" force called centrifugal, and a "fictitious" force called centrifugal. See Wiki links above, and this one:

http://en.wikipedia.org/wiki/Centrifugal_force#Fictitious_vs._reactive_force

And here another example comparing the two: As for "non existing": Some interpret "fictitious" forces as "not real" and just a math trick which gives correct predictions. However, the "real" forces are also just a mathematical abstraction that happens to give correct predictions. So it is a rather pointless philosophical exercise to argue whether the fictitious centrifugal real exists, or not.

AlephZero
Homework Helper
There is something else odd about all of this. My grade 12 physics notes and textbook talks a lot about centripetal force. But my university physics textbook only ever mentions a(rad), never once mentions "centripetal force".
That's the way it should be, IMO. At grade 12, you don't know enough math to do much except use arm-waving arguments for very simple physical situations.

Once you have the math tools to work with general equations of motion (and not restricted to rigid bodies moving with constant angular velocity) in arbitrary non-inertial coordinate frames, inventing logic-chopping terminology like "reactive centrifugal force" doesn't add any value IMO. (And in 30 years of reading peer-reviewed papers on the dynamics of rotating machinery, I've never seen it in print, outside of Wikipedia.)

Of course in the Lagrangian formulation of mechanics, most of the "forces" you talked about in grade 12 never appear anywhere in the math, so there is nothing to invent names for!

• 1 person
D H
Staff Emeritus
inventing logic-chopping terminology like "reactive centrifugal force" doesn't add any value IMO.
Well said.

And in 30 years of reading peer-reviewed papers on the dynamics of rotating machinery, I've never seen it in print, outside of Wikipedia.
Well said again. That replicates my experience. My take is that this concept has a small but rather vociferous following. Wikipedia is an avenue that lets those voices be heard.

A.T.
AlephZero said:
And in 30 years of reading peer-reviewed papers on the dynamics of rotating machinery, I've never seen it in print, outside of Wikipedia.

Wikipedia is an avenue that lets those voices be heard.
The problem seems that people conflate the two distinct forces and get confused. Wikipedia clears up the confusion by pointing out the two separate meanings.

Well said.

Well said again. That replicates my experience. My take is that this concept has a small but rather vociferous following. Wikipedia is an avenue that lets those voices be heard.
The good thing about Wikipedia is that sometimes they link their citations to the actual source. In this case they did.

I went to MIT's online learning material, http://72.30.186.176/search/srpcach...q&icp=1&.intl=us&sig=EY4r_US00mHSMQPwC1M37A-- . Near the bottom, it says that there is a reaction force to the centripetal force, but it has nothing to do with causing the object to move away from the center. So I think that the term centrifugal force is rejected because the origin of the term may have come from a false explanation of what causes the object to remain away from the center even though there really is a centrifugal force. So by definition, centrifugal force exists, but it is not the reason for the object's path it takes.

I realize that this is what a few posts had already explained, but they helped me understand the link above, which just says the same thing in a different way.

A.T.
So by definition, centrifugal force exists, but it is not the reason for the object's path it takes.
Depends which centrifugal force, which object and in which reference frame. But arguments about "reasons" get rather philosophical. The net force (and initial velocity) determine the path.

But my textbook also says that Newton's 3rd law implies that object A's force on object B will be equal and opposite to object B's force on object A. So I still don't understand how there can be an unbalanced force if Newton's 3rd law holds.
newtons laws exist in inertial frame of reference while pseudo force act due to non inertial frames...

on respect to question drawing FBD respect to car turning anticlockwise -----→centrifugal force

a pseudo force wrt car of a passenger inside

newtons laws exist in inertial frame of reference while pseudo force act due to non inertial frames...

on respect to question drawing FBD respect to car turning anticlockwise -----→centrifugal force

a pseudo force wrt car of a passenger inside
The link from MIT's resource material that I posted in post #17 explains how there is a centrifugal force, even in an inertial frame, but it is not the cause of the circular motion; only the centripetal force is the cause of the object's circular motion.

Depends which centrifugal force, which object and in which reference frame. But arguments about "reasons" get rather philosophical. The net force (and initial velocity) determine the path.
Sorry, I meant "causal reason" or just "cause".

Simon Bridge
Homework Helper
I think I see where the confusion lies - there are two uses of the word "centrifugal":
Any radially outward pointing force may be called "centrifugal" because that is what the word means.
However, what you'd commonly think of as "the centrifugal force", the sensation of something pulling you towards the outside of a curve, is an illusion - as your own reference emphasizes:

For instance, if you are riding in an automobile rounding a curve at high speed, you have to hold on to the edge of the seat to keep from sliding outward, and this gives you the sensation that something is pulling you to the outside of the curve, as though your weight had acquired an extra, centrifugal component. However, you are suffering from an illusion. There is actually no such centrifugal force pulling you outward ...
(My emphasis).
From: Dynamics of Uniform Circular Motion ch6 MIT "Pivot" Text Book.

This is in agreement with your text book - which is assuming common understandings.

I think I see where the confusion lies - there are two uses of the word "centrifugal":
Any radially outward pointing force may be called "centrifugal" because that is what the word means.
However, what you'd commonly think of as "the centrifugal force", the sensation of something pulling you towards the outside of a curve, is an illusion - as your own reference emphasizes:

For instance, if you are riding in an automobile rounding a curve at high speed, you have to hold on to the edge of the seat to keep from sliding outward, and this gives you the sensation that something is pulling you to the outside of the curve, as though your weight had acquired an extra, centrifugal component. However, you are suffering from an illusion. There is actually no such centrifugal force pulling you outward ...
(My emphasis).
From: Dynamics of Uniform Circular Motion ch6 MIT "Pivot" Text Book.

This is in agreement with your text book - which is assuming common understandings.
The semantics of this topic is down right evil!

Simon Bridge
Homework Helper
It's why nobody talks about centrifugal force if they can help it - it's too easy to get mislead.

The emphasis in HS level physics is getting you to unlearn common misconceptions as well as just to get used to using technical terms ... it's like when you learn that work require some movement by W=Fd right. So if you spend hours pushing a wall and it does not budge - you have done no work on the wall. But then - how come you are sweaty and tired? Have you really worked quite hard but it just does not cause anything to happen?

In fact, the question arises from different uses of the word "work".
In the technically correct approach - no work was done on the wall (the energy expended is internal to your body) and in the common approach, you've been working hard on that wall - for hours.

When you are doing physics, you should try to use the technically correct approach.
Just think "centrifugal force does not exist" and get on with it. You don't need the concept in order to do physics.

D H
Staff Emeritus