🚀 go-pugleaf

On Wed, 17 May 1995, Guntbert Reiter wrote:

> "Donald E. Simanek" <dsimanek@EAGLE.LHUP.EDU> wrote:
>
> >On Mon, 15 May 1995, Guntbert Reiter wrote:
>
> >> I prefer: Forces cause acceleration (not necessarily movement)
> >> while couples cause a torque (not a rotation).
>
> >You've still not gotten it right:
>
> >Net force produces acceleration (F = ma), while net torque produces
> >angular acceleration: (T = I*alpha) where T is net torque and 'alpha' is
> >angular acceleration.
>
> So, where`s the difference? (Although I think that we're arguing
> just for beeing as exact as possible, because the result  --
> linear +  angular acceleration  -- is doubted by neither of us.)

The issue is not merely semantic or pedantic, I think. When you said
"Forces cause acceleration (not necessarily movement)" that seemed to me
contradictory, for how can you have acceleration without movement? a =
d^2v/dt^2. It is true that you can have a zero instantaneous velocity
at an particular instant even though the acceleration is non-zero. An
example is the highest point of an object thrown straight up. Another
example is the time of maximum amplitude of a body in simple harmonic
motion. However, the word *movement* has a broader meaning. It is *not* a
synonym for velocity, and *not* a synonym for acceleration. It is not a
technical term with an operational or mathematical description, but is a
term like 'electricity' which refers to a broad class of phenomena. The
word 'movement' is likely not to be found in the index of a physics book.
Usually, we take 'movement' to mean 'a process or sequence of events
where a body changes its position.' By that meaning, I contend that if
you have a non-zero force on a body, you will have a process of movement,
even though at particular times during that process you may have zero
velocity.

Another problem I have with your terminology is this: You write:

        Forces cause acceleration
        Couples cause a torque

I'm comfortable with the 'Forces cause acceleration', though I prefer
avoiding the words 'cause' and 'effect' in physics. Still, I won't quibble.

But the two sentences, which seem to be constructed to emphasize
parallelism of thought, or perhaps analogous concepts, are *not* strictly
parallel in meaning. They *would* be if the second were worded:

        Torques cause angular acceleration

And for those who are following this discussion but are still a bit shaky
on the terms (rotation is often neglected in high school physics): Angular
acclleration is a *different* physical quantity from linear acceleration,
just as torque is a different thing than force. They have different
definitions, different laws, different behavior, etc.

I don't recall how couples got into this thread. It may have been my
fault. But couples aren't involved in the discussion of the force acting
on the stick isolated in space.

As to your phrase "Couples cause a torque" it is nearly tautological, for
a couple *is* a torque, one resulting from application of two
non-colinear equal and opposite forces. The word 'cause' here is
misleading. My previous comment, which you quoted, was less than elegant,
as you noted:

> >A couple is defined to be the torque produced by two *equal* size and
> >oppositely directed forces with a displacement between their lines of
> >action.  [Statement A]
....
> >The torque due to a couple is obviously Fd where F is the size of
> >either one of the forces and d is the perpendicular displacement between
> >them.   [Statement B]
>
> You're making contradictions in your paragraph:
> "A couple is defined to be the torque ..." vs. "The torque due to
> a couple is...". Between these two point of view I prefer the
> second: two forces with nonzero perpendicular displacement cause
> a torque and this causes an angular acceleration.

They aren't two points of view, Guntbert. I've numbered my two
statements, which you consider 'contradictory'. Statement [A] is a
definition, and a correct one at that, though use of the phrase 'parallel
and non-colinear' would have made it clearer and more concise.

Statement [B] probably bothers you because of the phrase 'Torgue *due to*
a couple'. I shall challenge you on this one, to tell me *specifically*
what fault you find with it. Bear in mind that the reason we give such a
combination of two forces the name 'couple' is that they have a very
special behavior: "The torque of a couple is the same wherever it is
applied to the body." This is not true of all torques. That is, the
effect of a couple on a body is the same wherever it is applied.

There is a semantic point that the world 'couple' has two uses. (1) It
describes the particular combination of two equal and opposite
non-colinear forces. (2) It describes the torque due to such a
combination of forces.

> >> be a linear acceleration of the CM. By Newton's laws (inertia...)
> >> we know that from this acceleration the CM should "feel" (I just
> >> can't remember the correct term) a corresponding force pointing
> >> in the opposite direction. So these two forces build a couple and
> >> produce a torque.
>
> >The CM (a mathematically computed point) can't "feel" anything. And
> >Newton's laws say nothing directly about the CM. Once you have *defined*
>
> Again you took me wrong: I know, that "feel" is a _very_ wrong
> term, but as English is not my language of daily use, I run out
> of "technical" term now and then, and I thought it would be clear
> from the context...

You were quite correct in putting quotes around the word "feel" to
indicate that it is being used in an unconventional, or possibly
imprecise manner. Some folks who have English as a *first* language are
not so careful. And I hope you do not take my comments inspired by your
message to be *criticisms*, for they are not so intended.

> About CM: We consider this as the point where the effect of
> mass-related forces is thought to ...(HELP: "touch" is wrong
> again).
>
> >I *assume* (though it's not at all clear from your paragraph above) that
> >the 'corresponding force in the opposite direction' refers to the reaction
> >force in Newton's third law. But, no, it can't, for the reaction force
>
> Of course it can't. But regardless of different "counting
> habits": You can express one law as: "acceleration and force are
> proportional". => Accelerating the CM leads by inertia to a force
> in the opposite direction....

Where does this => assertion come from? I am totally confused by it. At
first I thought the 'force in the opposite direction' was a reaction
force. But that doesn't add up. The reaction force would act on the agent
exerting the force on the stick. Now I wonder whether you mean the
'fictitious' force you'd put in to make F=ma when you do a problem in an
*accelerating frame of reference*. (In the same class with coriolis,
centrifugal, and such forces.) In any case, this seems totally
unnecessary in the present case: the problem of the force acting on the
stick in space.

> >applied to a stick in space, reaction force does not *in any way* enter
> >into this problem.
>
> yes, but inertia!

John Manlinkrodt posted a nice solution to the original problem which, as
I recall, does not mention the word inertia. I have conceptual difficulty
with phrases such as 'leads *by inertia* to a force' and 'mass-related
force'.

First off, what is the *definition* of inertia? Every word we use in
physics must have a definition somewhere, either an operational
definition (mass, length, time) or a mathematical one: a = dv/dt, etc.
What, then is the definition of inertia? Quick, look in your physics
books, folks. Can't find it? Find, perhaps a murky paragraph which isn't
clearly a definition? Then be suspicious of the use of the word. The
closest you may find is something like: "The reluctance (or resistance) of a
body to be accelerated". This is either anthropomorphic, or useless, for
it is not stated in a manner leading to calculation of the acceleration,
or the type of acceleration (linear, or angular). Just what is the
*measure* of inertia, and what is the law in which that measure can be used?

Most of you are ahead of me, I hope, and saying (to yourselves): "Mass is
the measure of inertia, in fact we have the term 'inertial mass' to
distinguish it from the far *different* concept 'gravitational mass'
which just happens in our universe to have the same measure as inertial
mass." Much philosophical discussion has transpired on *why* that
remarkable fact should be. But there's also *angular acceleration*. The
inertia associated with *it* is *moment of inertia*, I.

So inertia turns out to have broader meaning, being a descriptive term
covering several similar concepts. Not something one invokes in a
mathematical calculation or derivation.

As I recall, physicist Ernst Mach had a lot to say about the problem of
inertial and gravitational mass, and the philosophical problems
associated with these concepts.

Second: What *is* a 'mass-related force' and how is it distinguished from
forces which are not 'mass-related'? This is a concept I was never taught.

> >That motion will be a combination of translation and
> >rotation, a result of the applied force, and the torque associated with
> >that applied force.
>
> So you try to convince me of my own opinion. Please accept my
> apology for not being as clear as I wanted - language problems.

No apology necessary. Your posting was clearer than some others I've
seen. We agreed on the result, the outcome, of the problem of hitting the
stick at one end. But in physics we must convince our students that it's
not enough to get the right answer, but to have *some* correct and
defensible method for arriving at that answer, with every step clearly
and logically laid out. We should also remind students that their common
sense notions, their opinions, their hunches, and their feelings of
'rightness' and 'wrongness' are of no importance. Nature is not obligated
to conform to these. What matters is what can be tested against experiment.

Your posting, and the others, stimulated us to think more deeply about
this problem than we are used to doing. That's good for us all. It also
stimulated us to be more attentive to the words and terms we use.

        -- Donald