# Are fictitious forces necessary to solve certain problems?

1. Oct 8, 2011

### harrylin

It can be handy to ignore the Earth's rotation and simply work with the effective g', instead of accounting for g'=g+a; and similarly it may be handy to use Coriolis forces and so on for weather predictions. Nevertheless I assume that calculations with fictitious forces can always be reconverted in similar calculations without them, for the simple reason that they are based on Newtonian physics that does without them.

However, in recent discussions*, several people asserted that for particular cases it is necessary to introduce fictitious forces, or at least that introducing them significantly simplifies calculations of particular problems.

I invite those who agree with such claims to give specific examples here. Then we can put such claims to the test by trying to do similar calculations without fictitious forces.

2. Oct 10, 2011

### A.T.

Yes it does. If all your inputs are given in some non-inertial frame, and you need the results also in that frame, then what is the point in using some inertial frame for the calculation?

3. Oct 10, 2011

### Hootenanny

Staff Emeritus
I have to disagree with you there.
Very well. I'll let you offer your solution to the following question without referencing fictitious forces.

A rabbit of mass 1kg is sat still at the very edge of a circular roundabout, which has a radius of 1m. The roundabout is rotating at 1 rad/s. Compute the net force acting on the rabbit from the rabbit's point of view.

4. Oct 10, 2011

### mikeph

I would say that question is invalid because it depends subjectively on the rabbit's experience. In terms of objective, physical outcomes (eg. will the rabbit fall off or not), there would be no requirement for a non-inertial frame.

I tend to agree with the original poster. The only difference is the maths; our arbitrary choice of perspective cannot possibly affect the physics of the situation, because there is no causal connection between the problem itself and the person solving the problem.

5. Oct 10, 2011

### Hootenanny

Staff Emeritus
I don't quite understand - if you are referring to the rabbit's "conciousness", then simply replace rabbit by particle.
I didn't ask about physical outcomes. I explicitly asked harry to compute the net force in a non-inertial frame. There is no way to do this without moving to the frame in question.

6. Oct 10, 2011

### mikeph

The force "felt" by a particle can be disputed by different observers but the motion of that particle cannot be disputed, so I think you are giving a "trivial" solution to the problem and that OP's question should be re-worded.

Can you give me a physical scenario where it is not possible to predict the state of a system at a later time unless fictitious forces are used?

7. Oct 10, 2011

### harrylin

The point is to verify that your solution cannot be rewritten without fictitious forces, or at least, not without extremely complicating the calculation. Remember, I'm not making the claims here; but I'm willing to put your solution to the test.

PS: calculating the force that a rotating rabbit will measure is very basic Newtonian mechanics; D_H suggested that it becomes problematic for much more complex systems

Last edited: Oct 10, 2011
8. Oct 10, 2011

### D H

Staff Emeritus
The simple Newtonian physics that one does at the high school and freshman level in college does without inertial forces and torques. More advanced physics does not.

Nobody has said that in theory one could not solve such systems without the use of inertial forces and torques. In practice, there are many places where it is foolhardy (at best) to avoid the use of such devices.

1. A simple one to start with: Compute the forces due to the moon and the sun on a particle on the surface of the earth relative to the earth as a whole. This is easy to do in inertial and accelerating coordinates, but it serves as a nice starter.
2. This one is a bit tougher: Model the weather to the extent that you can predict the landfall of a hurricane or the likelihood of a tornado outbreak with some reasonable semblance of accuracy.
3. Even tougher: Model the effects on a hurricane as the hurricane passes over a set of mountainous islands in the Caribbean.
4. Simpler again: Pick up a book, preferably a hardcover book. Put a rubber band around the book so it won't fly open during the course of the experiment. Hold the book in one hand at the center of the bottom edge, with the cover of the book horizontal and facing upward and the spine of the book to the left. Toss the book upward, giving it a flip as you do so. Explain the motion of the book.
5. Same problem, but more generic: Explain why "the polhode rolls without slipping on the herpolhode lying in the invariable plane."
6. Problem #4 again, but this time with a softcover book given a flip out in space. The book will eventually stabilize to rotating about the axis normal to the cover of the book. Why? (Hint: It is well-known that rotations about the principal axes with the least and greatest moments of inertia are stable in the case of a rigid body. It is less well-known that there is only one stable axis of rotation, a rotation about the principal axis with the greatest moment of inertia, for a non-rigid body. Why?)
7. Develop the equations of motion for an articulated robot with three or more joints whose links are rigid bodies.
8. Develop the equations of motion for an articulated robot with three or more joints whose links are flexible bodies.
9. Develop the equations of motion for a satellite in a Lissajous orbit about the sun-earth L1 point.

Last edited: Oct 10, 2011
9. Oct 10, 2011

### harrylin

Sorry if my question was ambiguous (can you explain in what way?). Your rephrasing does match my question; however I also allow for the weaker claim about complexity, which I would like to put it to the test by comparing the lengths of the calculations.

10. Oct 10, 2011

### Studiot

11. Oct 10, 2011

### A.T.

12. Oct 10, 2011

### A.T.

Has anyone actually made that claim?

13. Oct 10, 2011

### D H

Staff Emeritus
No, you didn't.

All frames of reference are equally valid. Formulate the problem correctly and avoid errors along the way to the soluation and you will come up with the same answer regardless of the reference frames you use to solve the problem. If you formulate the problem incorrectly or make some mistake along the way, all you have demonstrated is that somewhere you made a mistake.

While all frames of reference are equally valid, for a given problem, some frames of reference are a lot easier to work with, are less likely to induce to human errors, and are less likely to induce mathematical errors such as caused by using finite precision arithmetic (e.g., a calculator or a computer that uses an IEEE floating point representation).

14. Oct 10, 2011

### mikeph

It wasn't ambiguous but I got the sense that it permitted solutions which did not match what you were seeking (such as "what forces are felt by a rabbit...").

My understanding is that inertial forces are never required to solve physical problems that are not specifically asking "what is the inertial force that is felt by...". Nobody is forcing you to use a rotating coordinate system, because the choice of coordinates does not affect the motion of a particle in reality (it necessarily cannot and if it does, there is an error somewhere).

I did some work on the three body problem and I can guarantee that a rotating frame will make things far easier, because it does, in a sense, eliminate much of the time-dependence of the bodies' positions. In a suitable frame, the Earth and the Sun are both at rest, and a third body (say, the moon) will have certain motions that you can analyse. Without this rotating frame, things get very very complicated very quickly. But I would not say that they get impossible.

15. Oct 10, 2011

### D H

Staff Emeritus
No one has made such a claim that I have seen.

Yep. This is my problem #9 in [post=3549961]this post[/post].

16. Oct 10, 2011

### Studiot

I didn't say they weren't.

No one has yet offered a correct answer to the question I asked.

Di you mean formulate the problem or formulate a solution?

I formulated the problem correctly, if you can allow me the faux pas of missing out part of the information in the first post, information that was supplied in the second.

17. Oct 10, 2011

### A.T.

Why don't you write again the complete question in one post, give us your two solutions (inertial frame, co-rotating frame with fictious forces) and show us how the later "will definitely get you the wrong answer"?

Edit by DH:

Last edited by a moderator: Oct 11, 2011
18. Oct 10, 2011

### Staff: Mentor

Fictitious forces will never get you the wrong answer unless you make a mistake.

19. Oct 10, 2011

### Staff: Mentor

Well, that is zero by definition of "the rabbit's point of view", so there is no need to actually calculate any fictitious forces. You would be better off asking for the force on a different object from the rabbit's point of view. Or asking for all of the forces rather than just the net force.

20. Oct 10, 2011

### Hootenanny

Staff Emeritus
I know. I was trying to eliminate as much computation as possible from the question so that the central point does not get obfuscated, as it has been in previous threads. The point is that if you are asked for a quantity in a non-inertial frame, you have no choice but to work with fictitious forces.

Perhaps you a right, I should have asked for a specific force acting on the rabbit. However, the point still remains: if you fail to account for the fictitious centrifugal force acting on the rabbit, then then net force will not vanish.

21. Oct 10, 2011

### Hootenanny

Staff Emeritus
The problem whilst trivial, requires the acknowledgement of the fictitious force present in the particle's frame. As I said above, I intentionally gave a trivial example in order to avoid confusion.
No, I cannot. Since one can always transform to an inertial reference frame, it is always possible to carry out computations without reference to pseudo-forces. However, if you need the answer in a non-inertial frame, pseudo-forces will appear when to transform to the non-inertial frame. There's no getting away from it.

22. Oct 10, 2011

### Staff: Mentor

Agreed, and I understand your pedagogical point also.

23. Oct 10, 2011

### D H

Staff Emeritus
This is a fallacious line of reasoning; it is a red herring. This is fallacious because nobody other than you the OP and you has made such a claim. I suggest (no, as a moderator, I insist) that this line of reasoning be dropped.

People use non-inertial frames for a number of reasons, but that it is impossible to predict the state of a system without the use of a non-inertial frame is not one of them. We use non-inertial frames because
• Their use makes the calculations at hand take on a much simpler form;
• Their use makes the numerical calculations more stable, more accurate (e.g., one doesn't have to resort to infinite precision arithmetic to compute the answer);
• The question requires that the answer be expressed in some non-inertial frame;
• And others. The above list is not exhaustive.

Besides, what inertial frame? Every reference frame we can construct is a non-inertial frame. As one of my bosses said to me long ago, "If you think there is such a thing as an inertial frame, name one."

24. Oct 10, 2011

### mikeph

I don't understand why you disagree with me since everything you have just said, I agree with. Why is it a fallacicous line of reasoning when it very closely follow's the original poster's question, and the person whom I quoted replied to me saying "I agree with you".

I don't know what claim that I apparently made that you're referring to either. I never said ficticious forces are NECESSARY, in fact everything I've written is arguing against this, as you've just done.

25. Oct 10, 2011

### Hootenanny

Staff Emeritus
Now you are playing word games.

I did not agree with you. I merely admitted that one can always use inertial frames to describe the state of a system. The question I quoted was not a statement and therefore I couldn't agree with it!