View Full Version : Re: Torque or Moment or Angular force...

Paolo De Leva
11-12-2007, 05:21 AM
Dear subscribers,

Ton van den Bogert suggested to close this discussion "unless someone has
.. actual new material". I agree with him. I submitted this contribution
while his message was still being processed (8 November 2007 22.04), and he
posted it as an attachment to another message with a modified subject header
("one more...") and format. I have cleaned and completed the text and
resubmit it now with the correct subject heading and format. My contribution
meets Ton's requirement, because it describes an alternative point of view
(see subject header). I suggest that those who want to comment on this do
that by sending a message to me. After two weeks from now, I will post on
BIOMCH-L a compilation. This way, we will not bother too much those who are
not interested in this topic.

Paolo de Leva.

-----Original Message-----

Dear subscribers,

Ton van den Bogert is right: "it would be great if we could agree on this"
(i.e. on using "moment" rather than "torque", as suggested by John Paul).
However, in this case we have two separate and widely accepted standards.
Standards, not opinions. Here is an alternative point of view, explained in
ten points:

1) There has been a widely known precedent: SI (Systeme International
d'Unites) versus the British system. The SI was born in the 18th century;
its mother was the French revolution, it became adult in the late 20th

2) Today it is not yet completely accepted in US, but it will. May be in 10,
50, 100 or more years, but it will. Indeed, nobody can honestly deny that
the SI is the best system, not even those who keep using a different system.
They do so just because they are used to. The change is too expensive for
them: a desired good that they cannot afford to buy.

3) I am not going to compare BIOMCH-L with the France of the 18th century.
This is not the point.

4) The point is that "torque" versus "momentum" is a war that nobody can
win. Both standards have strong weaknesses! (see for instance the
etymological notes in my previous messages; in addition, consider that
"torque" comes from the Latin "torquere" = "to twist").

5) To win a war, a third, less questionable name is probably needed. For

"angular force" or "rotational force", as opposed to "(linear)
force" (notice that in the late 18th century Joseph Louis
Lagrange introduced the "generalized force", 6 numbers
including force and moment of force), or
"rotor" (if John Paul says that a torque produces only torsion,
and a motor produces motion, please indulge me and let me say
that a rotor can produce a rotation, even though this word is
already used to indicate the rotating part of an engine), or
"gyrator" (etymology similar to "rotor"; already used in
electronics to indicate an impedance inverter)

5b) However, the war will never be won by "nihilating the enemy". No new
terminology (not even the word "torque") will ever completely substitute the
expression "moment of a force", because "(nth) moment of a quantity
about..." is used in physics to indicate the multiplication of a quantity by
a distance or power of a distance, as in:

(First) moment of mass, used to compute CM position.
(Second) moment of mass = moment of inertia.
(First) moment of the quantity of motion = angular momentum.
(Second) moment of area, used by structural engineers to
estimate an object's resistance to bending.

5c) The expression "(nth) moment of ... about" is also used in mathematics
to indicate a similar concept [see "http://en.wikipedia.org/wiki/Moment
(mathematics)"]. For instance:

"Second moment about the mean" = variance.

6) Do we know how many scientists (not only biomechanists) are used to use
or chose to use the word torque as a synonym of moment in their studies
(including physicists)? Every year, thousands of (native and foreign)
students learn physics in USA, or studying textbooks written by US
physicists. The influence of USA universities on the scientific community is

7a) I suspect that "moment" was the word initially used by everybody. My
guess is that "torque" was later adopted by some influential physicists
because they did not like the aspecificity and ambiguity of the word
"moment" (it comes from the Latin "movimentum" = "movement", it also means
"instant"; what has that got to do with rotation?). This change was
intentional, not casual!

7b) There was also another important change, which is probably related:
Newton called "quantity of motion" the quantity that we now call (in
English) "linear momentum". And "moment of the quantity of motion" the
quantity that we now call "angular momentum". Not difficult to imagine that
this change was welcome by everybody! Again, "quantity of motion" is too
generic. As you see, the rationale is similar.

7c) The conflict between two different usages of the word "torque" is not
enough to discourage physicist or engineers. It exists also for the
expression "moment of inertia"; many structural engineers keep referring to
the "second moment of area" as the "moment of inertia" (although relating
the word inertia to an area is definitely questionable)! For solving this
conflict, rather than just cancelling the improper usage, they invented this
horrible specification: "area moment of inertia" versus "mass moment of

8) Notice that the SI prescribes the name of the unit ("Newton metre"), but
as far as I know it does not give a preference about the name of the
quantity ("moment of force" or "torque").

9) A representative international committee (ISO) is the only organization
that can solve this problem. And most likely, the committee will be mainly
composed of physicists.

10) An optimistic observation: at least this is not a very expensive change.
A new non-questionable name for this quantity may be accepted faster than
the whole SI. There is no need of a revolution.

10b) Pessimistic: possibly, other terminological "fixes" are needed in other
chapters of physics. A change in a single word will not be accepted, if
other questionable words or expressions (such as "area moment of inertia")


It does not matter if we agree on using the word "moment". We are not going
to convince the other half of the word. Terminology evolves, but changes are
expensive and nobody will ever accept questionable changes; etymologically,
both "moment" and "torque" are questionable words.

Moreover, I suppose that the river of history is flowing in the opposite
direction! We are just advocating a return to the past. We are not starting
a revolution, but resisting against a revolution started a long ago.

With my kindest regards,

Paolo de Leva
Department of Human Movement and Sport Sciences,
Istituto Universitario di Scienze Motorie
Rome, Italy