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View Full Version : Re: Centrifugal Force

Paolo De Leva
12-19-2000, 04:18 AM
Dear subscribers,

it's amazing that Ton and I can disagree about one single and extremely simple point. I agree about 99% of what Ton wrote in his latest contribution on this topic (dated Dec 18 2000). And Ton, believe me, I really enjoied your clarity and insight in this part. But the remaining 1%, on which we disagree, happens to be the only point on which I wanted to reach an agreement, and about which I wrote my latest contribution.

My point was clear and simple (in my honest opinion, of course). Briefly: accelerometers do use inertial frames.

This point was associated with another similar and simple concept:

>"unfortunately, you can't just forget the inertial (Newtonian)
> frame when you use D'Alembert's principle

because you use the "real" acceleration to compute the inertial force: Fi=-m*a.

In his reply, Ton described his equations, maintaining they are perfectly correct (of course), and you only need to plug in them accelerometer data to solve them. This part belongs in the 99% on which we agree (believe me, I have never doubted that, Ton). By the way, I enjoied the formal perfection of Ton's explanations about his equation [the transposition to make F and A column vectors, for instance].

Ton, and dear readers, will you forgive me if I'll joke a little to make this discussion more stimulating? May I reveal the human face of this debate? That might not be British, but I want to confess that my first reaction after reading Ton's answer was disappointment. Sincerely, I thought something like "how can such a wonderful mind believe that accelerometers measure accelerations in their own local non-inertial frame? Isn't it obvious that an accelerometer has zero acceleration in its own local frame?"...

Of course this first thought was too simplistic. I read Ton's message late in the night, and after reading it I was puzzled. I have been thinking and thinking to its contents before falling asleep. Today, I kept reading Ton's message again and again, in the attempt to figure out the reason why he could't agree with me. Reading Ton's message I understood what follows:

1) Ton knows accelerometers better than his wife :-).
2) Ton knows that an object (e.g. the accelerometer, and the rigid body to which it is attached) is perfectly static relative to a reference frame attached to it (therefore has no acceleration).
3) Ton knows that non-inertial frames, and apparent forces "existing" in these frames "are absolutely necessary... if the equilibrium equations are to be valid" (see Necip Berne's nice contribution to this discussion on BIOMCH-L). So null acceleration (i.e. equilibrium) is not only obviuos, but our explicit purpose, i.e. what we absolutely want to obtain, when we use non-inertial frames.

Is there anyone who would like to help me to understand Ton's conclusions, starting from the above assumptions or proving that they are wrong? I would be happy to be convinced that they are wrong (if they were actually wrong, of course), because I consider a discussion successful only if agreement is reached on the main points, and I have spent so much time in this discussion....

>"Yes", ...[the acceleration data obtained with the accelerometer is]... "relative to the inertial frame,
but it is always combined with gravity and rotated to the moving frame".

OK, I agree. This is another part belonging in the 99% on which we agree. The clear point is that he says "relative to the inertial frame". So, you can see that my first judgement about Ton's message was obviously wrong.

Here's the 1% on which we disagree:

> ...you do not need the Earth or any other inertial
> frame, as long as you use accelerometers to determine the force field
> due to the reference frame being non-inertial.
[...omissis...]
> I would say non-inertial frames are needed
> because usually we can only collect data in a non-inertial frame,

I ask you, Ton, and all readers: should we conclude that the force field in a non-inertial frame is different from zero? (I remind you Necip Berne's statement about the need for equilibrium, i.e. net force = 0).

Well, what's the meaning of Ton's statements then? Did he maintain that accelerometers can measure apparent-imaginary-fictitious (i.e. inertial) forces?

MY ANSWER: No, I don't think so. Ton perfectly knows that an accelerometer is "simply a mass attached to a little force transducer" (or some equivalent device embedded in an integrated circuit).

About accelerometers, I have seen a few of them, and I can say I know them better than Ton's wife. So, the only difference between me and Ton is that I don't know Ton's wife.
From the little I know (I am not joking here; I have seen them, but never used) I deduce that the accelerometer measures the contact forces made by its "body" on that little mass, which are always equal to the net external force minus the weight of the small mass. Am I right, Ton? I wonder how should we describe the net external force and the weight of the small mass. Ton, should we call them imaginary or real forces? And the difference between them (which is what you called "the force field due to the ref. frame being non-inertial") is a real force or an imaginary force?

Well, now I am helpless. Both my attempts to understand the true meaning of Ton's statements failed. Ton, or someone else, please help me.

I am sure Ton and most of the BIOMCH-L subscribers can answer to my previous question without my help. But maybe some students are reading my message (yes, I know, I am optimist: Ton might be my only reader), and I would like to help them to give their own answer:
1) Real (Newtonian) forces are always produced by an object on the environment (e.g., the accelerometer body or the planet earth).
2) Imaginary-apparent-fictitious-inertial-D'Alembertian forces are not exerted by any external object, and by the way, for that reason there's no reaction to these forces (i.e. they don't meet Newton's third law).

By the way, some of you were referring to Einstein's equivalence principle saying that gravity cant' be distinguished from inertial forces. But only one wrote Einstein's equivalence principle correctly: Dr. Kris Kirtley. Others did not consider that gravity is exerted by a mass which exists in the environment, and which you can see, identify and measure, while inertial forces are exerted by nothing. They were missing a small yet important part of Einstein's enunciation, i.e. its last four words:

"..cannot be distinguished...by any 'interior' experiment."

I beleive the word 'interior' here is important, isn't it? If you know you are on the earth, you know there must be a gravitational attraction, and if you can measure the Earth mass, and the position of its center of gravity, you can even compute the intensity and direction of your weight. So, if you can analize the 'exterior' environment, the equivalence principle doesn't apply. You can tell gravity from other foces. I didn't study Einstein's theories in detail; I'm just guessing. Kris, did I interpret Einstein's words correctly?

Referring to Ton's example about weather forecasting, please let's not forget we need to know the angular velocity of the earth and the radius of rotation of the air particles to compute the value of the Coriolis and centrifugal forces thei are acted upon. Ton, I have a latter question for you: were these data measured in a "fixed" - inertial reference frame or in a non-inertial reference frame?

With regards,

Paolo de LEVA

University Institute of Motor Sciences
Sport Biomechanics
P. Lauro De Bosis, 6
00194 ROME - ITALY

Telephone: (39) 06.367.33.522
FAX/AM: (39) 06.367.33.517
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