# Centrifugal Force: Is it Radially Outwards?

• mabs239
However, it is still a mystery to me as to what exactly provides the outward force against gravity on the stone.

#### mabs239

I read that the centrifugal force acts radially outwards on a stone being revolved by a person with a string. But I have just fallen into the confusion as what keeps the stone at a constant height when one is revolving it above one's head. Surely there must be a vertical force too, equal to the weight of the stone which prevents it from falling down.

Now is it right to say that centrifugal force is radially outwards or I have some misconceptions

Thank you

mabs239 said:
I read that the centrifugal force acts radially outwards on a stone being revolved by a person with a string. But I have just fallen into the confusion as what keeps the stone at a constant height when one is revolving it above one's head. Surely there must be a vertical force too, equal to the weight of the stone which prevents it from falling down.

Now is it right to say that centrifugal force is radially outwards or I have some misconceptions

Thank you

It is right to say that centrifugal force is radially outward, but centrifugal force acts on the string, not on the stone. Centripetal force acts radially inward on the stone. This is what provides the vertical component of force against gravity and the horizontal component of force keeps the stone from traveling on it's "preferred" straight-line path. What is a little confusing here is that there is no outward force on the stone.

elect_eng said:
It is right to say that centrifugal force is radially outward, but centrifugal force acts on the string, not on the stone. Centripetal force acts radially inward on the stone. This is what provides the vertical component of force against gravity and the horizontal component of force keeps the stone from traveling on it's "preferred" straight-line path. What is a little confusing here is that there is no outward force on the stone.

Why the centrifugal force don't act on the stone. If you are right then the stone should not run away if the link between the stone and the rope breaks near the stone. Which certainly is not the case. Are should I interprate it as that, during motion centrifugal force acts only on string but it is instantaly transmitted to stone to go away when the link breaks?

If the centripetal force acts radially inward, how it counter acts the action of gravity. Free body diagrams shold take the gravity into consideration as well, which I have never seen in any textbook.

It is still a puzzle to me as what is there to counteract the gravity...

The stone rises because the misaligned linear forces creates a torque. The upper end of the string experiences an inwards force (from the persons hand), and the lower end of the string an outwards force (reaction force from stone).

Hi there,

elect_eng is right in his definition. This is also why the centrifugal force is called imaginary. It is not a real force acting on the stone. If you let the rope go, or if the rope is cut, you will not see the stone go away from the circular motion, but parallel to it.

Cheers

Jeff Reid said:
The stone rises because the misaligned linear forces creates a torque. The upper end of the string experiences an inwards force (from the persons hand), and the lower end of the string an outwards force (reaction force from stone).
I left out the other part. The string is at an angle, so the tension in the string includes a downwards component on the upper end of the string and an upwards component on the lower end of the string.

mabs239 said:
I read that the centrifugal force acts radially outwards on a stone being revolved by a person with a string. But I have just fallen into the confusion as what keeps the stone at a constant height when one is revolving it above one's head. Surely there must be a vertical force too, equal to the weight of the stone which prevents it from falling down.

Now is it right to say that centrifugal force is radially outwards or I have some misconceptions
Realize that the string is at an angle with the horizontal. The vertical component of string tension balances the weight of the stone; the horizontal component of string tension provides the inward centripetal (not centrifugal) force.

In standard usage, "centrifugal force" is a fictitious force that arises from analyzing the motion in a rotating frame of reference. Forget about it. There are only two "real" forces acting on the stone: The string tension and gravity.

Doc Al said:
In standard usage, "centrifugal force" is a fictitious force that arises from analyzing the motion in a rotating frame of reference. Forget about it. There are only two "real" forces acting on the stone: The string tension and gravity.

I agree with this. However, there is a non-standard usage "reaction centrifugal force" which is a real force in the non-rotating frame. This is simply defined as the reaction force to the centripetal force. The string exerts centripetal force on the stone, but the stone exerts a reaction force on the string. This is a real force necessary to have the string under tension. Another example of confusing terminology.

elect_eng said:
I agree with this. However, there is a non-standard usage "reaction centrifugal force" which is a real force in the non-rotating frame. This is simply defined as the reaction force to the centripetal force. The string exerts centripetal force on the stone, but the ball exerts a reaction force on the string. This is a real force necessary to have the string under tension. Another example of confusing terminology.
Using the term "centrifugal" to describe the force that the stone exerts on the string is non-standard and confusing. So don't use it.

Doc Al said:
Using the term "centrifugal" to describe the force that the stone exerts on the string is non-standard and confusing. So don't use it.

I agree with that, but the non-standard usage still persists and seems relevant to the OPs confusion.

Here is a link that describes the distinction between the real and fictitious forces.

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

elect_eng said:
I agree with that, but the non-standard usage still persists and seems relevant to the OPs confusion.

Here is a link that describes the distinction between the real and fictitious forces.
I am well aware of the distinction. (And this very issue has been discussed here ad nauseam.)

If you look at the OP's first sentence:
mabs239 said:
I read that the centrifugal force acts radially outwards on a stone being revolved by a person with a string.
It's pretty clear that he's talking about forces on the stone and is making the usual error in viewing centrifugal force as a real force. Bringing up the non-standard usage of centrifugal force as a "reaction" force on the string is irrelevant and only adds to the confusion.

mabs239 said:
But I have just fallen into the confusion as what keeps the stone at a constant height when one is revolving it above one's head.

You mean with your hand (holding the string) below the stone?

Not possible unless you're cheating.

elect_eng said:
Here is a link that describes the distinction between the real and fictitious forces.

http://en.wikipedia.org/wiki/Centrifugal_force
That Wikipedia article is a prime example of why Wikipedia is not to be trusted. Wikipedia has more than its fair share of articles with a tinge of crackpot, fringe, or out-dated concepts. Unless one is already versant in the field, there is no way to know whether an article is legitimate or is a stinking pile of stuff.

Let's look at what is happening to the stone from four different perspectives. To simplify things, I'll assume one end of the string is attached to a thin rotating vertical pole. The other end of the string is attached to the rock. The length of the string is l and the the angle between the string and the horizontal is θ. The pole is rotating with angular velocity ω. The rock revolves about the pole with this same angular velocity. The four different perspectives:
1. Kinematic point of view, inertial observer
The rock is undergoing uniform circular motion in a horizontal plane that intersects the pole at a point l sin θ below the attachment point on the pole. Call the intersection between the pole and the horizontal plane in which the rock is "central point". The radius of the circle traced by the rock is l cos θ. The rock's angular velocity about this central point is ω. Uniform circular motion means the rock is accelerating toward the central point. The magnitude of this acceleration is ω2r = ω2l cos θ. Multiplying by the rock's mass m yields the centripetal force. What does this centripetal force mean? Not much. Centripetal force is tautologically defined as the centripetal acceleration times mass. The exact same centripetal force results in many completely different circumstances.

Note well: There is no centrifugal force in this point of view.

2. Dynamics point of view, inertial observer
The string is under some tensile force T. The forces on the rock are gravity Fg=mg directed downward and this tensile force, directed toward the attachment point. The vertical and horizontal component of this tensile force are T sin θ (directed upward) and T cos θ (directed inward). The vertical and horizontal components of the net force on the rock are T sin θ - mg and T cos θ. Reconciling this with the kinematic point of view, T sin θ - mg = 0 and T cos θ = mω2l cos θ. Thus T = mω2l and sin θ = g/T = g/ω2l. This point of view adds a lot to the kinematic point of view. Now we know the tension in the string and have derived the angle θ. In the kinematic point of view, the angle θ is a given. In the dynamics point of view, the angle is a consequence of the motion.

Note well: There is no centrifugal force in this point of view.

3. Kinematic point of view, rotating observer
This point of view uses a rotating frame in which the rock is stationary. The origin of the frame is some point on the pole (which point doesn't matter). Since the frame is rotating and since rock is located some distance r=l cosθ from the rotation axis, there is a centrifugal force acting on the rock. This centrifugal force is directed away from the pole and has magnitude ω2r = ω2 l cosθ. The rock is stationary, so (a) there is no coriolis force and (b) the net apparent force is zero. In a rotating frame, the net apparent force is the sum of the net real force plus the fictitious forces. The net real force acting on the rock is thus ω2r directed inward.

Note well: There is no centripetal force in this point of view. The rock isn't moving in this point of view.

4. Dynamics point of view, rotating observer
The net real force on the rock is the sum of the tensile force from the string and the gravitational force. Reconciling this with the kinematics result yields the exact same results as does the inertial dynamical point of view.

Note well: There is no centripetal force in this point of view. The rock isn't moving in this point of view.

Finally, note that there is no "reactive centrifugal force" in any of the points of view.

Doc Al said:
Bringing up the non-standard usage of centrifugal force as a "reaction" force on the string is irrelevant and only adds to the confusion.

That's a matter of opinion. I brought it up in the hope that it might clear up the confusion. If I was wrong about that, so be it. But, only the OP can judge if I confused him more, or helped him understand better.

Doc Al said:
I am well aware of the distinction.

I know you are aware of the distinction. Did you really doubt that? The reference was obviously for the OP.

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Doc Al said:
I am well aware of the distinction. (And this very issue has been discussed here ad nauseam.)

By the way, I have a sincere question about this. Since there seems to be a real distaste to use the term centrifugal force as a real force, what is the preferred terminology to talk about this force? As an electrical engineer working in the field of motors and generators, the term centrifugal force is often used to describe the force that outer parts of a rotating system place on the inner parts. Should I say "reaction force to centripetal force" and avoid the term centrifugal force, or is there an existing term that describes the force without confusion?

D H said:
Finally, note that there is no "reactive centrifugal force" in any of the points of view.

So, I conclude that one of Newton's laws is not correct. Apparently, the law that every force has an equal and opposite force is not valid? What keeps the string under tension? The string pulls on the stone. Should not the stone pull on the string?

If you don't like he terminology, fine, I don't like to argue about terminology. What is the correct terminology to describe the real force that the stone puts on the string to keep it under tension? I've gotten into this debate a number of times and am tired of it. Please tell me the correct word to use to avoid arguements.

mabs239
Doc Al said:
I am well aware of the distinction. (And this very issue has been discussed here ad nauseam.)

If you look at the OP's first sentence:

It's pretty clear that he's talking about forces on the stone and is making the usual error in viewing centrifugal force as a real force. Bringing up the non-standard usage of centrifugal force as a "reaction" force on the string is irrelevant and only adds to the confusion.

Has the centrigugal source idea been discarded? I have seen some other threads on CF force like: https://www.physicsforums.com/showthread.php?t=231139 and found the discussions interesting. I am so thankful to all of you guys for being helpful, but still I am so much confused.

elect_engg,
Thanks for staying here. Your last post gives me the idea that you are doubtful too. I didn't think this theory so hard to understand at first.

tiny-tim,
I don't understand your point. Why should I be cheating? It is quite possible to keep the stone rotating within a plane fairly parallel to the Earth, or not?

DH,
Quote: "To simplify things, I'll assume one end of the string is attached to a thin rotating vertical pole."
I have got the instinct that the stone won't rotate as it does when a person rotates it by hand. Are you satisfied with the experimental setup? In my opinion, the result would be that the rope will be wound around the pole in the shape of a coil.

And why are you using the rotating pole? Definitely a person doesn't keep his hand/arm rotating. Is the rotation idea just to start motion in one particular direction? How would the pole provide centripital force.

Dear Fellows,
Which physics book/website do you people recommend to study the up-to-date Physics ideas and concepts. I realize that I have many more misconceptions.

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mabs239 said:
elect_engg,
Thanks for staying here. Your last post gives me the idea that you are doubtful too. I didn't think this theory so hard to understand at first.

I'm not doubtful of my understanding of the physics or how to do the calculations. However, I am doubtful of the correct terminology that doesn't offend people. In high school, I was taught that centrifugal force is the reaction force to centripetal force. In college, the ideas of a rotating reference frame (noninertial frame) having ficticious forces due to the accelleration of the frame itself (Coriolis force, Euler force), were made clear. (and also referred to as centrifugal force)

As an electrical engineer, I don't really have to worry about the terminology. If I need to do a calculation or derivation, I just do it.

Apparently, there is a desire to classify centrifugal force as only a fictitious force needed in noninertial reference frames. If so, I'm asking what is the accepted terminology for the real force that is the reaction to centripetal acceleration. Mind you, this real force is not a force on the stone in your example. I made this clear in my first post.

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mabs239
mabs239 said:
It is quite possible to keep the stone rotating within a plane fairly parallel to the Earth, or not?

With your hand below the plane, no.

elect_eng said:
So, I conclude that one of Newton's laws is not correct. Apparently, the law that every force has an equal and opposite force is not valid? What keeps the string under tension? The string pulls on the stone. Should not the stone pull on the string?
Enough with the hyperbole, already!

Newton's third law does not apply to net force. It applies to individual forces. In this case, the individual forces are gravity and tension. The equal but opposite reaction to Earth's gravity pulling the rock downward is the upward gravitational force exerted by the rock on the Earth. The equal but opposite reaction to the string pulling on the rock is the rock pulling on the string, directed at an angle θ with respect to the horizontal.

What is the correct terminology to describe the real force that the stone puts on the string to keep it under tension? I've gotten into this debate a number of times and am tired of it. Please tell me the correct word to use to avoid arguements.
The force between the string and rock is electrostatic in nature. If you insist on applying a name to it, I guess you could call the force the rock exerts on the string a tensile reaction force. Then again, not everything needs a name.

Calling this reactive force "centrifugal" is wrong. The centripetal force (a net force, not a real force) is purely horizontal. The force the rock exerts on the string has a vertical component and has a different magnitude than that of the centripetal force. Calling this real reactive tensile force the reactive centrifugal force is a misnomer.

D H said:
Calling this reactive force "centrifugal" is wrong. The centripetal force (a net force, not a real force) is purely horizontal. The force the rock exerts on the string has a vertical component and has a different magnitude than that of the centripetal force. Calling this real reactive tensile force the reactive centrifugal force is a misnomer.

Yes, I understand you. What I should have referred to as "reactive centrifugal force" would be the horizontal component of the reactive tensile force (I didn't say that correctly before): that is, the force opposite the centripetal force. Some people find this concept useful, and I think this is what they mean when they say "centrifugal force" in this context. If it's considered wrong to say that, who am I to argue. I generally avoid the term, but when other people speak it, I know what they mean and don't debate them about it. Of course, they are usually "customers" so that is good policy perhaps.

You are basically saying that the centripetal force is also not a real force. So, another point of confusion is what is meant by a "real" force. Again, I have no interest to argue about the words and meanings, but your meaning is clear to me, and I basically agree with it.

Thank you for the explanation.

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The definitions for the adjective form of these terms:

centripetal - proceeding or acting in a direction toward a center or axis
http://www.merriam-webster.com/dictionary/centripetal

centrifugal - proceeding or acting in a direction away from a center or axis
http://www.merriam-webster.com/dictionary/centrifugal

So although physicists have an issue with the term "centrifugal force", it would seem to be valid usage in common English, in this case for the force the stone exerts onto the string.

In a more generalized example, a rocket engine could be used to change the shape of the orbit of a satellite with a thrust perpendicular to the direction of travel and in the plane of the orbit; the thrust could be centripetal (inwards) or centrifugal (outwards). During the period while thrust was active, the path would include a spiral component.

elect_eng said:
You are basically saying that the centripetal force is also not a real force. So, another point of confusion is what is meant by a "real" force.
Centripetal force is just a label for the net force that produces the centripetal acceleration. It's not a separate "real" force itself. In this example, the only forces that would appear on a free body diagram for the stone are string tension and gravity. (A common error among freshmen is to show a third force labeled "centripetal force" on such a diagram.) As stated before, the horizontal component of the force exerted by the string on the stone (an electrostatic force) provides the centripetal force.

In another sense, the forces acting on the stone are "real" since they have agents--something that exerts the force. The string exerts a force on the stone and the earth exerts a force on the stone. So, in that sense, the forces that produce the centripetal acceleration are real, agented forces. (As opposed to centrifugal force, which has no agent.)

I thought D H gave an outstanding explanation.

Jeff Reid said:
The definitions for the adjective form of these terms:

centripetal - proceeding or acting in a direction toward a center or axis
http://www.merriam-webster.com/dictionary/centripetal

centrifugal - proceeding or acting in a direction away from a center or axis
http://www.merriam-webster.com/dictionary/centrifugal

So although physicists have an issue with the term "centrifugal force", it would seem to be valid usage in common English, in this case for the force the stone exerts onto the string.
There's nothing wrong with using a dictionary to learn the etymological roots and everyday meaning of words. (But to use an ordinary dictionary as a scientific reference is even lamer than using Wiki. ) In this case the common meaning of "centripetal" and "centrifugal" are completely consistent with their scientific usage. (Often, perfectly good common words are co-opted by science and given a very different technical meaning. Look up the common meaning of words like work, energy, weight, mass and see how you do.)

If you want to play the dictionary game, don't stop too soon:
centrifugal force -- the apparent force that is felt by an object moving in a curved path that acts outwardly away from the center of rotation
http://www.merriam-webster.com/dictionary/centrifugal force

That's not too bad. Not crisp enough to pass a physics test, but not bad.

The dictionary on my desk (American Heritage) is better:
Centrifugal force: The component of apparent force on a body in curvilinear motion, as observed from that body, that is directed away from the center of curvature or axis of rotation.

I like it.

(And note that neither dictionary entry mentions anything about "reaction" forces. )

Doc Al said:
Note that neither dictionary entry mentions anything about "reaction" forces
True, but the stone force is related to (caused by) it's acceleration. Ignoring the angula apects, the rock could be hanging from a string attached to roof of some box undergoing constant acceleration and get similar results. In some cases the equal and opposing force is related to the inertia "reaction" of an accelerated mass.

besides... that would be centripetal force, not centrifugal.

Doc Al said:
In another sense, the forces acting on the stone are "real" since they have agents--something that exerts the force. The string exerts a force on the stone and the earth exerts a force on the stone. So, in that sense, the forces that produce the centripetal acceleration are real, agented forces. (As opposed to centrifugal force, which has no agent.)

I thought D H gave an outstanding explanation.

I thought he gave an outstanding explanation too.

However, what is still not clear to me is why centripetal force would be classified differently than centrifugal force. At least, if one adopts the definition that centrifugal force is the reaction to centripetal force, they would seem the same classification to me.

Sure in this example of the stone, centripetal force acts on the stone and centrifugal does not. However, (ignoring the angle and component issues for ease of discussion) suppose we look at the first line element of the string attached to the stone. That line element is allowed to have tension due to the equal and opposite forces from the stone (centrifugal) and the next line element of the string (tension). All other line elements have tension only from the tension of the neighboring line elements, accept the last one at the persons hand.

What is the problem with the above view point? Is it just a matter of people not wanting to define centrifugal force that way, or is there something inherently wrong with this viewpoint?

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Consider the stone being whirled in a vertical circle rather than a horizontal circle.The situation can be analysed for any point in the circle but it is quite instructive to consider the topmost point.At the top the weight plus the tension provide the centripetal force both of these forces acting towards the centre of the circle.If the stone is whirled more and more slowly the tension reduces and at a particuler speed will become zero.At this speed the weight only is providing the centripetal force there being no outward pull on the string at all.

yeah, that makes perfect sense.. but it would be a good idea to make sure one knows the difference between the two before confusing the reasoning and theory. Centripetal is the vector force (curved or lateral direction) and cetripetal is the inertial force (the tangent).. can't really be arsed to read the whole post sorry :)

There are two forces acting on the stone: The outward horizontal centrifugal force Fhoriz; and the downward gravitational force Fvert. When you twirl a stone around your head in a Goliath sling, the downward slope of the string is about tan(Fvert/Fhoriz).

Bob S said:
There are two forces acting on the stone: The outward horizontal centrifugal force Fhoriz; and the downward gravitational force Fvert. When you twirl a stone around your head in a Goliath sling, the downward slope of the string is about tan(Fvert/Fhoriz).
Regardless of the status of the nomenclature imbroglio over whether there is such a thing as a reactive centrifugal force, there is no real centrifugal force acting on the rock, period. The net force acting on the rock *must* be inwards for the rock to undergo circular motion.

D H said:
Regardless of the status of the nomenclature imbroglio over whether there is such a thing as a reactive centrifugal force, there is no real centrifugal force acting on the rock, period. The net force acting on the rock *must* be inwards for the rock to undergo circular motion.
But that's the point of calling the foce the rock exerts on the string a "reactive" force,: it's the inertial reaction due to the acceleration caused by the real net force. When the real forces don't cancel, then there is a net real force, and the acceleration corresponds to the net force / the inertia (mass in the linear case), and the "reactive forces" are simply a means to describe the reaction to the net forces in compliance with Newtons 3rd law about forces only existing in pairs. It's like a method of accounting to get the forces to sum up to zero, the real forces and the reactive (to acceleration) forces.

Jeff Reid said:
But that's the point of calling the foce the rock exerts on the string a "reactive" force,: it's the inertial reaction due to the acceleration caused by the real net force. When the real forces don't cancel, then there is a net real force, and the acceleration corresponds to the net force / the inertia (mass in the linear case), and the "reactive forces" are simply a means to describe the reaction to the net forces in compliance with Newtons 3rd law about forces only existing in pairs. It's like a method of accounting to get the forces to sum up to zero, the real forces and the reactive (to acceleration) forces.

Newtons third law does have the forces occurring in pairs but it also requires the forces to be :
1.of the same type
2.equal in size
3.opposite in direction
The above three criteria are not met when considering the centripetal force on the stone and any pull on the string.

Jeff Reid said:
But that's the point of calling the foce the rock exerts on the string a "reactive" force,: it's the inertial reaction due to the acceleration caused by the real net force. When the real forces don't cancel, then there is a net real force, and the acceleration corresponds to the net force / the inertia (mass in the linear case), and the "reactive forces" are simply a means to describe the reaction to the net forces in compliance with Newtons 3rd law about forces only existing in pairs. It's like a method of accounting to get the forces to sum up to zero, the real forces and the reactive (to acceleration) forces.

The only points of talking about the reactive force (for me) is to acknowledge one of Newton's laws and to name a force reponsible for internal stresses in a rotating system. The outer parts of the rotating system place a force on the inner parts. I won't even use the "bad" word here. Just acknowlege that the force is there and is sometimes important.

However, there is no balancing of outward and inward forces on the stone in this example. There is NO centrifugal force on the stone! This makes sense because there is no equilibrium in the horizontal plane. The vertical forces are in equilibrium so you want the upward component of string tension to balance gravity. But you do not want the horizontal force to balance, otherwise the stone wouldn't move and we would all be wondering why the stone was just floating there.

Jeff Reid said:
But that's the point of calling the foce the rock exerts on the string a "reactive" force,: it's the inertial reaction due to the acceleration caused by the real net force.
This gets to the heart of the problem. The net force is not necessarily a "real" force, defined as a force with a causative agent. The only case in which the net force is a real force are the trivial case in which zero or one real forces act on an object.

Newton's third law applies to real forces with causative agents, and only to these real forces. Pretending that the net force is a real force can get you in trouble. It might, for example, make you think there exists a third law reaction against it. This particular problem exemplifies that. The third law reactions are the rock pulling the Earth upwards and the rock pulling the string outwards and downwards. There is no horizontal reactive force.