Physics Help Forum What precisely are "inertial" forces?

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 Aug 22nd 2017, 07:08 PM #1 Senior Member   Join Date: Nov 2013 Location: New Zealand Posts: 510 What precisely are "inertial" forces? This concept seems to be hanging me. It's used in a lot of D'Alembert problems and even on various texts on the web. The wiki page on "D'Alembert's principle" points to a page called "fictitious forces". https://en.wikipedia.org/wiki/Fictitious_force Except the wiki page on this starts talking about accelerated frame's of references which aren't the sort of problems I have been working on. So some questions...Are D'Alembert forces real or fictitious forces ? What makes these forces special and why do we need them? What advantage is D'Alembert's method over just applying Newton's second law? Does it make sense to use D'Alembert's method without employing generalised co-ordinates?
Aug 22nd 2017, 07:24 PM   #2
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 Originally Posted by kiwiheretic This concept seems to be hanging me. It's used in a lot of D'Alembert problems and even on various texts on the web. The wiki page on "D'Alembert's principle" points to a page called "fictitious forces". https://en.wikipedia.org/wiki/Fictitious_force
WARNING! Whomever wrote that page made a mistake. The inertial forces from D'Alembert's principle are not the same thing as inertial forces in the Wikipedia page it links to.

 Originally Posted by kiwiheretic Except the wiki page on this starts talking about accelerated frame's of references which aren't the sort of problems I have been working on.
Exactly. Didn't I mention this to you before? The term inertial force is an overloaded term which means it has two different meanings. Context determines which one you want.

 Originally Posted by kiwiheretic Are D'Alembert forces real or fictitious forces ?
Real

 Originally Posted by kiwiheretic What makes these forces special and why do we need them?
One inertial force which is referred to as the Coriolis force is because its what causes certain weather phenomena. See: https://www.nationalgeographic.org/e...riolis-effect/

Another inertial force of renown is the centrifugal force. Its what gives the spaceship inhabitants in the movie "Martian" the effect of gravitational field so they can walk around that part of the ship. It's for reasons like these that they were of great importance to Einstein when he was working on GR

 Originally Posted by kiwiheretic What advantage is D'Alembert's method over just applying Newton's second law?
In certain instances it can make the formulation of the mathematical problem easier to formulate.

 Originally Posted by kiwiheretic Does it make sense to use D'Alembert's method without employing generalised co-ordinates?
Not really. You can certainly do it. You just make it less generalizable and thus harder to apply.

 Aug 22nd 2017, 07:36 PM #3 Senior Member   Join Date: Nov 2013 Location: New Zealand Posts: 510 So then does D'Alembert's principle have anything useful to say about problems involving inclined planes, rolling balls, frictionless sliding blocks and pulley's where no accelerated frames are involved?
Aug 22nd 2017, 07:43 PM   #4
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 Originally Posted by kiwiheretic So then does D'Alembert's principle have anything useful to say about problems involving inclined planes, rolling balls, frictionless sliding blocks and pulley's where no accelerated frames are involved?
I don't know what you consider useful. As I said, sometimes it just makes solving a problem easier. Is that useful?

 Aug 22nd 2017, 08:49 PM #5 Senior Member   Join Date: Nov 2013 Location: New Zealand Posts: 510 By making a dynamics problem a static one by putting the problem in an accelerated frame of reference?
Aug 22nd 2017, 09:08 PM   #6
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Do you recall the book I mentioned by Lanczos on the variational principles of mechanics? Its a great book on D'Alembert's principle and addresses what you wish to know.

I should state that while I have read and studied D'Alembert's principle of virtual work in graduate school it was a very long time ago and I don't recall much of it. I did reread that part of Lanczos and recommend you find it online and read that section. I cannot stress that enough. Let me quote part of it here so you get how great that text is. From page 93
 D'Alembert's principle is fundamental in still another respect; it makes possible the use of ,moving reference systems, and is thus a forerunner of Einstein's revolutionary ideas concerning the relativity of motion, explaining - within the scope of Newtonian physics - the nature of those "apparent forces" which are present in moving systems.
The author also points out that Hamilton's principle can be derived from D'Alembert's principle by a mathematical transformation. Hamilton's principle is restricted to holonomic systems whereas D'Alembert's principle applies to both holonomic and non-holonomic systems. My back is killing me now so I'll let you look those terms up yourself.

By the way. When I suggest taking a look at a particular text/book its always for a very good reason. Some books explain certain things exceptionally well. I'd quote them but it takes time and its painful for me to post lately since my HDTV bit the dust. I used it as a monitor which made things easy to read and thus post. Now I'm restricted to smaller monitor and have to sit on the floor making it very painful for me to post right now. The idea here is that reading that text is better all around rather than having me quote it or try to recall things from that dusty part of my memory.

On another note - I have three cats. Two are brothers. Right now one is licking the butt of the other. Now that is what I call brotherly love. Lol!

Last edited by Pmb; Aug 22nd 2017 at 09:27 PM.

 Aug 22nd 2017, 09:33 PM #7 Senior Member   Join Date: Nov 2013 Location: New Zealand Posts: 510 Thanks, I'll try the Taylor's book first and work through some of the problems in Chaper 6 Calculus of Variations, Chapter 7 Lagrange Equations and possibly Chapter 8 Two Body Central Force problems and then decide where to from there. I am hoping this pursuing the "holy grail" of "not relying on co-ordinate systems" is really worth it and the advantages of generalised co-ordinates hasn't been oversold.
Aug 22nd 2017, 10:16 PM   #8
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 Originally Posted by kiwiheretic Thanks, I'll try the Taylor's book first and work through some of the problems in Chaper 6 Calculus of Variations, Chapter 7 Lagrange Equations and possibly Chapter 8 Two Body Central Force problems and then decide where to from there. I am hoping this pursuing the "holy grail" of "not relying on co-ordinate systems" is really worth it and the advantages of generalised co-ordinates hasn't been oversold.
Generalized coordinates is extremely important.

Aug 22nd 2017, 10:25 PM   #9
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 Originally Posted by kiwiheretic Are D'Alembert forces real or fictitious forces ?
It's not a good idea to refer to inertial forces as "fictitious". There's significant caution in the physics literature against doing that, although this is a point of disagreement among physicists.

The point on thinking of inertial forces as not being "real" is addressed in that text I mentioned, i.e. The Variational Principles of Mechanics - 4th Ed., Cornelius Lanczos, Dover Pub., page 98.
 Whenever the motion of the reference system generates a force which has to be added to the relative force of inertia I’, measured in that system, we call that force an “apparent force.” The name is well chosen, inasmuch as that force does not exist in the absolute system. The name is misleading, however, if it is interpreted as a force which is not as “real” as any given physical force. In the moving reference system the apparent force is a perfectly real force, which is not distinguishable in its nature from any other impressed force. Let us suppose that the observer is not aware of the fact that his reference system is in accelerated motion. Then purely mechanical observations cannot reveal to him that fact.
From Introducing Einstein's Relativity, by Ray D'Inverno, Oxord/Clarendon Press, (1992) page 122
 Notice that all inertial forces have the mass as a constant of proportionality in them. The status of inertial forces is again a controversial one. One school of thought describes them as apparent or fictitious which arise in non-inertial frames of reference (and which can be eliminated mathematically by putting the terms back on the right hand side). We shall adopt the attitude that if you judge them by their effects then they are very real forces. [Author gives examples]

Last edited by Pmb; Aug 22nd 2017 at 10:27 PM.

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