# Why isn't centrifugal force drawn on a free body diagram?

Discussion in 'Physics' started by tjohnson, Apr 6, 2015.

1. ### tjohnson Thread Starter Active Member

Dec 23, 2014
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When a free body diagram of a ball being swung in a circle is drawn (example), only tension and weight are drawn on it. I understand that the centripetal force equals tension plus weight at the top of the circle, and tension minus weight at the bottom of it, but there must also always be an equal centrifugal force because of Newton's 3rd Law. Since this force also comes into play, why isn't it drawn on the free body diagram? To me, the diagram seems incomplete without showing it, yet I don't recall ever seeing centrifugal force shown on this type of free body diagram.

Last edited: Apr 6, 2015
2. ### WBahn Moderator

Mar 31, 2012
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Centrifugal force is a pseudo force. It does not exist. If anything, what you think of as "centrifugal force" is the force of the ball acting on the string. When you draw a free body diagram you draw the forces acting ON the body and not the forces that the body exerts on other things.

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3. ### Papabravo Expert

Feb 24, 2006
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As long as the rope is taut and the orbit is a circle it serves no useful purpose. Slow the angular velocity down so the rope goes slack and it still would not be relevant because the tension in the rope disappears, and the orbit is no longer a circle. The actual force on the ball and the radial component of acceleration, derived from the change in direction of the velocity vector, point in the same direction as Newton's Law requires

Last edited: Apr 6, 2015
4. ### WBahn Moderator

Mar 31, 2012
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What would be relevant? Centrifugal force? If the rope goes slack then there is only a single force acting on the ball (ignoring air friction), namely gravity, and the ball is in ballistic flight until such time as the rope goes taut again. There is no centrifugal force at play. If there were, then you would need to explain the mechanism by which this force comes to be applied to the ball. It is either a contact force or a force at a distance. If the rope is slack, then there are no contact forces (again, ignoring friction) and there are only four possible forces at a distance -- gravitation, electromagnetic, and the strong and weak nuclear forces. So which one is "centrifugal force".

5. ### Papabravo Expert

Feb 24, 2006
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I realized that in the process of composing and editing. Check the revision.
Your point was the correct one -- it is forces on the body and not the body's effect on the surroundings that are relevant.

6. ### tjohnson Thread Starter Active Member

Dec 23, 2014
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Thanks, that makes sense. It also makes sense then why in a free body diagram of a box sitting on a floor, the normal force exerted by the floor on the box is drawn, because although it too is a pseudo force which does not exist, it differs in that it does act on the body (the box).

7. ### WBahn Moderator

Mar 31, 2012
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The force of the floor acting on the box very much is a real force. It is not a pseudoforce.

The notion of "centrifugal force" is a mistaken notion that comes from viewing things from a non-inertial reference frame. Think of yourself sitting in a car going around a curve. Even though you know you moving and you know you are going around a curve, your senses tell you that some "force" is pushing you up against the door (assuming you are sitting on the outside of the curve) or, if you are on a merry-go-round (the small ones at playgrounds) that some "force" is pushing you outward from the center trying to throw you off. But that is not the case at all. There is no force pushing you against the door, the door is pushing against you because it is causing you to deviate from the straight line path you would otherwise take.

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8. ### Papabravo Expert

Feb 24, 2006
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See the following for a description of the non-inertial frame of reference defined by an angular velocity vector Ω. It includes the Coriolis force, the centrifugal force, and the Euler force.

http://en.wikipedia.org/wiki/Inertial_frame_of_reference
Sorry: I sometimes suffer from Attachmenesia

Last edited: Apr 7, 2015
9. ### studiot AAC Fanatic!

Nov 9, 2007
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There is nothing mistaken about centrifugal force.

Yes it is imaginary.
But quite deliberately, not mistakenly.

However it is a transformation and, like all transformations, it must be used correctly.
In particular alternative methods must not be mixed.
Any more than you would mix integrating directly and using a Laplace transform.

The purpose of imaginary forces is to reduce a dynamic system, not in equilibrium, to a static one which is in equilibrium.
Doing this allows the solution by the laws of equilibrium in place of Newton's laws of dynamics.

And just like a Laplace or any other transform the method only works if we apply the inverse transform at the end of the analysis.

The method was introduced by D'Alembert and has wider application than just circular motion. Indeed NSASpook has just posted a thread about quaternions that does this in CGI.
The method is alternatively called D'Alembert's hypothesis or D'Alembert's Theorem.

Note D'Alembert was also responsible for a simplifying, non complex, solution to the wave equation, of much use to electrical engineers.
This latter is called D'Alembert's Method.

So the answer to the original question is that centrifugal force will appear on a free body diagram if D'Alembert's Theorem is employed to transform the system to astatic one.
Otherwise it is not shown because it does not exist in the original dynamic situation.
In order to have acceleration Newton's laws require a resultant force.

10. ### WBahn Moderator

Mar 31, 2012
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While it, and several other pseudoforces, can be used very effectively in several non-inertial reference frames, the way that it is commonly used by many, many people is, most definitely, a mistake.

11. ### alfacliff Well-Known Member

Dec 13, 2013
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so centrigrigugal force is imaginary? it is a representation of what ever force is holding the object in orit around its center point, whether force exerted on a rope or gravity. is there no pull on the rope? is there no pull on the center point at all? even now they are identifying stars with planets around them by their wobble induced by planets in orbit.

12. ### studiot AAC Fanatic!

Nov 9, 2007
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Life is never as easy as this.
Linear motion is supposed to be easier than curved
So consider the following:

Two experiments are proposed where a tractor unit tows an aircraft using a heavy duty spring balance and a suspect coupling.
It is known that the total rolling resistance is 4MN.
It is suspected that the coupling is only good for 15MN in tension.
The tractor can exert up to 20MN of tractive effort (pull).

In the first experiment, starting from standing, the tractor pulls steadily on the aircraft until the scale reading on the spring balance reads 10MN.

Describe what happens. What force does the tractor accelerate the coupled pair with?

In the second experiment the tractor is to be run up until either the maximum pull is exerted or the coupling breaks.

Again describe what will happen.

What is the tension in the coupling?

13. ### WBahn Moderator

Mar 31, 2012
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You are confusing centrifugal (outward acting) force with centripetal (inward acting) force. The force on the object holding it in orbit is centripetal force. There is NO centrifugal force acting on the object (in an inertial reference frame). If you want to talk about the force acting on the rope (or on the other object in the case of force at a distance) then it is reasonable to call that centrifugal force. But the TS is very clearly talking about the free body diagram of the object being swung on a rope, NOT on the rope and NOT on the object at the other end of the rope.

14. ### WBahn Moderator

Mar 31, 2012
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I can't figure out what you are trying to describe. The fact that you are using an aircraft implies that there is some angle in the tow line since, presumable, it is not dragging the airplane along the ground. So what is the angle? What is the drag acting on the aircraft? What does "pulls steadily" mean? Steadily usually implies constant and unchanging, but it would seem to make more since to mean "steadily increasing" here.

15. ### studiot AAC Fanatic!

Nov 9, 2007
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I am trying not to complicate things, the pulls are horizontal.

You can think of a locomotive and a train if you prefer, I was simply trying to bring the question up to date a bit with the plane.

It is the forces in the coupling I want to concentrate on.

Last edited: Apr 7, 2015
16. ### alfacliff Well-Known Member

Dec 13, 2013
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an inward acting force holding in orbit? what holds it out in orbit? and why is centripital force confused with gravity? a rope is centripital force?

17. ### WBahn Moderator

Mar 31, 2012
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You actually seem to be having the same misconception that is so common when thinking about circular motion.

Let's use the example of a ball being swung on a string. Let's neglect air resistance and let's either have this be in a horizontal plane and fast enough so that the effect of gravity is minor or imagine this being done out in space so that it is negligible.

Would you agree that the only reason that this ball is staying in the orbit is because of the force acting on it by the string?

Would you agree that strings can pull but that they cannot push?

So, if there is some outward acting force holding it in orbit, where is that force coming from and how it is being applied to the ball?

18. ### studiot AAC Fanatic!

Nov 9, 2007
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Almost the same question applies to the coupling I have mentioned.

It was no idle theory. Too many railway 'engineers' in the past under-designerd coupling as a result of this real mistake.[/quote]

19. ### WBahn Moderator

Mar 31, 2012
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I would think that the design of a railroad coupling is going to be dictated not by steadily applied loads but by the impact loads associated with the taking the slack out of the couplings. Am I wrong on that? Given the masses involved, it wouldn't take much slack to result in a huge impact as the front part of the train gets moving and then suddenly tries to get the-still-motionless rear part of the train moving. I imagine the couplings are designed with some kind of compliance mechanism to soften this.

One thing that I have often wondered about was when you have a push/pull train (no helper engines in the middle) that is moving along the front couplings are in tension (the front half of the train is being pulled by the lead engines) while the rear couplings are in compression (the back half of the train is being pushed by the tail engines). So somewhere near the middle is a coupling that is largely unloaded. In theory you could decouple those two cars and not notice any difference. In reality, of course, things aren't nice and smooth and so the location of where the tension/compression transition is will constantly be moving. That would seem to have the potential to result in a lot of chatter and impact on the middle couplings. Is that the case? Is it a problem? If so, how is it managed? Or are the loads that are involved at that point low enough that the couplings simply deal with the impact chatter without appreciable damage?

20. ### studiot AAC Fanatic!

Nov 9, 2007
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Railroad cars have mating buffers that absorb the push.
The coupling links are slack in such circumstance. They are never in compression.

Going back to my example.

There is 5MN of rolling resistance so nothing happens until the tractor/loco exerts 4MN+.

At this point extra applied (pull) force will start to accelerate the load (up to 10MN in my case).
So the maximum accelerating force is 10MN

However the coupling is taught in tension to the tune of (10 + 4 )MN = 14 MN.

We know what real agent provides the 10 = 4 in the case of the loco (one side of the tension pull)

But the coupling can only be in 14MN tension if there is and equal and opposite pull on the other side.
But the rolling resistance is only 4MN, so what provides the other 10?