# The Myth of Fictitious Force

You are making fundamental mistakes.

Centrifugal force is NOT acting on the slider. Slider is not rotating. (ω=0 -> FC=ω²R=0) That means, whatever's pulling it, is not centrifugal force.

The force acting on the slider is the tension in the arm connecting slider to rotator. The tension on the rotator side of the arm is the centripetal force that keeps rotator moving in circles. Rotator is accelerating towards the slider, not away. That means the force acting on it is towards the slider. And centrifugal force would have to push rotator away from slider. So centrifugal force is not acting on rotator either.

If you go into coordinate system attached to the slider, there is centrifugal force acting on the rotator, but you are obviously in an accelerated frame of reference. Motion of slider is not uniform, so you expect Fictitious forces.

The way you check if there is a net external force is you look at acceleration of center of mass, and it's clear from all of the above, and even your own analysis, that acceleration of CM in the x-direction is zero. That means, no net force in x-direction. That means, centrifugal force is not involved.

If you look in the y-direction, there is net acceleration and net force. But I account for it by showing that this force comes from the rail. Again, centrifugal force not involved.
k-2, I have gone over your Langrangian derivation and I am beginning to have doubts about the constancy of w. I found a lot of algebraic errors, starting with the eqm's, at the very top. There are a lot minuses for pluses and vice-versa and these ripple down in your other derivations. Plus, I don't see lamba3 in your substitution of the eqm for x1 into the eqm for x2. Also, I'm not sure how you seperated the equations, I would like to see the rigorous proof. And did this prove the constancy of w before phi at pi/2 or did this prove it for all angles of the rotator? For pre-phi, it is trivial to prove it is constant, you don't even need Langrangian. The tough proof would be after pi/2. If you could prove the constancy of w for all angles, after correcting your errors, I would appreciate it very much. Once you prove the constancy you can stop there in the analysis. I attempted to prove it myself, but again there are a lot of errors, so I did not proceed.

This doesn't seem right to me. The action and reaction act on different bodies. So if there is, for example, gravitational force on a planet, the reaction is force on the star. The centrifugal force arises as a purely inertial effect.
I agree. As an electrical engineer, I've found that if I want to pick a fight with a physicist, in the fastest way possible, I don't need to slap him in the face with a glove. Just mention the term "reaction centrifugal force", and the fight is on.

If you have a weight on a string and you whirl it around your head, the string places centripetal force on the weight and a centripetal reaction force on your hand. Now, if you look at an element of the string itself, there is a force on each side of the length element. The tension in the string is created by centripetal force and reaction centripetal force. In other fields, and I was even taught this in high school, the reaction force is sometimes called "centrifugal", and it is a "real" force, whatever you call it. This is a completely different animal from the "ficticious" centrifugal force like Coriolis etc.

The thing is that physicists have drawn a line in the sand and have said, "DO NOT CALL REACTION TO CENTRIPETAL FORCE A CENTRIFUGAL FORCE". I guess they feel this is better to avoid confusion. I see no reason to fight with them about this. It's just terminology. If we accept this, then centrifugal force is always "ficticious", as much as I hate the word ficticious in this context.

I've never had any significant issues doing a Newtonian mechanics problem, whether in an inertial or non-inertial reference frame, and I never sweat about the terminology, but I have to say that this thread has confused me more than any real-world classical mechanics problem ever could.

As an engineering student, I was taught by my physics teachers that there are 4 real fundamental forces and my engineering teachers promised I would need to deal with only two of those in real engineering problems, - so far so good as I hit the halfway point in my career. So, we can ask, is reaction centripetal force real? Well, yes it is real because it is electromagnetic in the case of a weight on a string, or gravametric in the case of two astronomical bodies orbiting each other. It seems to me that the inertial force due to a noninertial reference frame can not be electromagnetic, nor can it be gravametric, and I don't think anyone is going to claim it is a nuclear force.

A fallback position is to cite Einstein's gravity and note that he established laws valid in any reference frame. In effect, he banished the "inertial frame" and sent it into the wastelands. So, now with inertia and gravity equated, does centrifugal force gain the status of real force by proxy? I say no, since it's the other way around. Gravity now roams the badlands too.

The last fallback position would be to ask, "What will a unified field theory say about inertia, and could it allow us to call inertial force real?" I don't know how to answer that, nor do I know if it is even a meaningful question to ask.

A fallback position is to cite Einstein's gravity and note that he established laws valid in any reference frame. In effect, he banished the "inertial frame" and sent it into the wastelands. So, now with inertia and gravity equated, does centrifugal force gain the status of real force by proxy? I say no, since it's the other way around. Gravity now roams the badlands too.

The last fallback position would be to ask, "What will a unified field theory say about inertia, and could it allow us to call inertial force real?" I don't know how to answer that, nor do I know if it is even a meaningful question to ask.
Good thoughts. I say we can call inertial force real if we can demonstrate that it can do everything else that a "real" force can do. One reason inertial forces was classified as fictitious was because there was no other physical body one could relate it to. In Newtonian mechanics it is axiomatic that contact forces come in pairs. So, if you are in a rotating frame, and you have a body that is on a radial track, if the body is unrestrained, it will start accelerating away from you. (Assume you are at the axis of the rotating frame.) Now relative to your frame "something" is causing the body to accelerate away from you. Einstein pointed out this something could be viewed as a gravitational field. Now, if you reached out and grabbed the body and restrained it from moving away from you, you would feel a force. Conventional terminology would call this a fictitious force because you cannot associate another body with it, as required by Newton's third law, that is experiencing an equal and opposite force. Time out. This conventional terminology is ignoring the advances of modern physics. Forces can also manifest when a body is accelerating relative to a field. There is a lot of literature out there that relates the manifestation of inertia to the presence of a field in space. Now in the case of general relativity, the field is space itself being curved. (One interpretation.) Another interpretation says its the metric of space that determines gravity-inertia. You have the Machian inertia interpretation of general relativity. You have the formalism of Dennis Sciama, you have gravitomagnetic models, you have the scalar field of Brans-Dicke, you have models that relate inertia to the vacuum energy, and you have an interesting effect tested recently by the Gravity Probe B experiment-- the frame-dragging effect predicted by Lense and Thirring. Some would argue this has a Machian interpretation of the cause of inertia. All of these theories suggest that inertia arises out of a coupling of objects in a ubiquitous field in space. I think the frame-dragging effect is worth considering. If you want to see the latest data and more info about frame-dragging, go to the Gravity Probe B website. They have some interesting videos on the topic. Now, back to the example of the rotating frame. The recent test results of Gravity Probe B suggests that relative to the cosmic mass of the universe which could be viewed as a "hollow shell", the relative rotation of the frame "inside" and with respect to this hollow shell, generates a local frame-dragging effect within the rotating frame which causes the manifestation of both a Coriolis and centrifugal effect. When you restrain the body from moving, some theorists would argue its the frame-dragging effect that is causing the force-- not a fictitious force. But as I said, one way to judge if inertia is real is to test its consequences. I have done this in an experiment. If you want to see a video of it, you'll have to look back through this thread. The bottom line is the experiment showed that the speed of the center of mass of a rotator-slider system increased with respect to a laboratory frame. The only "force" possible that could cause this increase in speed was an inertial force. There is a well-established law in mechanics, known as Euler's first law. It states that only an external force acting on a system can change the velocity of the center of mass of the system. The conservation of linear momentum also requires this. Thus inertial force is real in the sense that it can qualify as an "external" force to a system and impact the momentum of the center of mass of the system. Also, the experiment isn't just demonstrating a local effect. It is indirectly confirming that a global field must exist in space that accounts for the test results. Time will tell which theorist is correct. Incidentally, I lean toward the vacuum energy explanation in combination with a general relativistic metric interpretation of inertia.

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D H
Staff Emeritus
For crying out loud, e2m2a! There are these nice little things called paragraphs that help people read and understand what you write. Please do try to use them.

For crying out loud, e2m2a! There are these nice little things called paragraphs that help people read and understand what you write. Please do try to use them.
Ok. I'll use spaces between paragraphs. Thanks for pointing it out.

For crying out loud, e2m2a! There are these nice little things called paragraphs that help people read and understand what you write. Please do try to use them.
You're lucky you found one that understands the concept, "paragraph." I usually just ask people to "hit the 'enter' key once in a while," with the hope they'll reflexively do it at logical points in their stream of consciousness.

D H
Staff Emeritus
Ok. I'll use spaces between paragraphs. Thanks for pointing it out.
Use line returns, two of them, between paragraphs. Continue to use only spaces and this thread is locked. Continue to write in the style you have been using and this thread is locked.

One of the rules of this forum is no posting of personal theories. This thread looks a lot like a personal theory, but I can't really tell because I can't read/parse what you wrote.

You are making fundamental mistakes.

Centrifugal force is NOT acting on the slider. Slider is not rotating. (ω=0 -> FC=ω²R=0) That means, whatever's pulling it, is not centrifugal force.

The force acting on the slider is the tension in the arm connecting slider to rotator. The tension on the rotator side of the arm is the centripetal force that keeps rotator moving in circles. Rotator is accelerating towards the slider, not away. That means the force acting on it is towards the slider. And centrifugal force would have to push rotator away from slider. So centrifugal force is not acting on rotator either.

If you go into coordinate system attached to the slider, there is centrifugal force acting on the rotator, but you are obviously in an accelerated frame of reference. Motion of slider is not uniform, so you expect Fictitious forces.

The way you check if there is a net external force is you look at acceleration of center of mass, and it's clear from all of the above, and even your own analysis, that acceleration of CM in the x-direction is zero. That means, no net force in x-direction. That means, centrifugal force is not involved.

If you look in the y-direction, there is net acceleration and net force. But I account for it by showing that this force comes from the rail. Again, centrifugal force not involved.
Actually, a typical analysis would show its the y-compoment of the centripetal force in the positive y-direction that accounts for increase in velocity of the center of mass of the rotator in the positive y-direction. However, the centripetal force is one force of a pair of forces as mandated by Newton's third law. The other force is the centrifugal reactive force acting on the axis attached to the slider.

Since this force pair is internal to the system, by the conservation of linear momentum and Euler's first law, it is impossible for these forces to impact the center of mass of the system in any way.

Also, the constraint forces of the rails can be completely removed, and yet an increase in the speed of the center of mass of the system would be observed. This could be done by having a dual-rotator system in space-- one rotator rotates counter-clockwise, the other clockwise. Initially, the left end of the slider could be up against an object (space shuttle). The two rotators could initially be at 9 o'clock. At some point in time each rotator could be given an impulse, one in the positive y-direction, the other in the negative y-direction.

Since there is no friction. the dual-rotator-slider system would began to move to the right immediately when one rotator is at 12 o'clock and the other rotator is at 6 o'clock. Essentially, everything analyzed for the single rotator system would apply. The speed of the center of mass of the system would increase, but there would be no rail constraint forces to account for it.

One last afterthought. In a previous post, I doubted the constancy of the angular velocity of the rotator. But I have found a simple, straightforward way to prove it, invoking the conservation of linear momentum.

The speed of the center of mass of the system in the positive x-direction at 6 o'clock is expressed as:

(mrrw)/(mr+ms) = constant (1).

where, mr is the mass of the rotator, ms is the mass of the slider, r is the distance from the axis of rotation to the center of mass of the rotator, and w is the angular velocity of the rotator.

By the conservation of linear momentum the speed in the positive x-direction must remain constant as the system begins to move to the right, beginning at 6 o'clock. (We assume no friction.) Now, mr,ms, and r is constant. (The r term is a holonomic constraint of the system and is a constant.) Thus, in order for the speed to stay constant to comply with the conservation of momentum, w must always be constant. q.e.d.