I was wondering, why in Newtonian physics torque is called "torque" while in static mechanics they call it "moment"?
I prefer by far the term "torque", for not only it sounds strong, but also instead of moment, the correct synonym of torque is moment of force.
Torque is the informal, practical man's way of calling this thing; the moment of force is the more quantitative, scientific term which is better at expressing the formula $$ \vec \tau = \vec r \times \vec F $$ The position $\vec r$ and the cross product, for this specific case, are responsible for the words "moment of" while $\vec F$ is the force.
A similar addition of "moment" to other terms is the way to express other quantities although the terminology isn't quite systematic. For example, the angular momentum $\vec L = \vec r \times p$ is derived from the momentum $\vec p$ (well, the word "moment" was already inside "momentum" so people added "angular" instead because "moment of momentum" sounds awkward). The moment of inertia is a quantity like $I = mr^2$ which differs from the (inertial) mass $m$ by powers of $r$, too.
When trying to understand why words are used to describe certain things, it often helps to look at their etymology. For moment:
moment mid-14c., "very brief portion of time, instant," in moment of time, from O.Fr. moment, from L. momentum "movement, moving power," also "instant, importance," contraction of *movimentum, from movere "to move" (see move). Some (but not OED) explain the sense evolution of the L. word by notion of a particle so small it would just "move" the pointer of a scale, which led to the transferred sense of "minute time division." Sense of "importance, 'weight' " is attested in English from 1520s. Phrase never a dull moment first recorded 1889 in Jerome K. Jerome's "Three Men in a Boat." Phrase moment of truth first recorded 1932 in Hemingway's "Death in the Afternoon," from Sp. el momento de la verdad, the final sword-thrust in a bull-fight.
Moment would appear to come from Latin for "moving power". The works of Archimedes including On the Equilibrium of Planes which contains statics and levers, was translated into Latin by Gerard of Cremona (c. 1114–1187 AD). Therefore it seems likely that Archimedes used "moving power" to describe the effect of a lever in moving a mass on the other end, and being proportional to the product of the applied force and its distance from the fulcrum on the other end.
Turning our attention to torque ;)
torque "rotating force," 1884, from L. torquere "to twist" (see thwart). The verb is attested from 1954. The word also is used (since 1834) by antiquarians and others as a term for the twisted metal necklace worn anciently by Gauls, Britons, Germans, etc., from L. torques in this sense. Earlier it had been called in English torques (1690s).
And it seems likely that it comes from latin "to twist".
I would conclude that torque was meant to describe a force that twists an object about its main axis, while a moment rotates the main axis. Think of a long cylindrical steel rod where the main axis runs along its center. For objects with no obvious main axis, one person's torque is another's moment depending upon what the main axis is chosen to be.
I have been wondering a long time about that particular question too, and I think there is no simple answer. For example, at Wikipedia they consistently use symbol $\vec{\tau}$ and explain:
http://en.wikipedia.org/wiki/Torque#Terminology
In US mechanical engineering, the term torque means 'the resultant moment of a Couple', and (unlike in US physics), the terms torque and moment are not interchangeable. Torque is defined mathematically as the rate of change of angular momentum of an object. The definition of torque states that one or both of the angular velocity or the moment of inertia of an object are changing. And moment is the general term used for the tendency of one or more applied forces to rotate an object about an axis, but not necessarily to change the angular momentum of the object (the concept which in physics is called torque).
However, in ISO 80000-4 they use symbol $\vec{M}$ and call moment of force $\vec{M} = \vec{r} \times \vec{F}$, while they call torque only a component of moment of force "directed along a Q-axis": $T = \vec{M} \cdot \vec{e}_Q$
IMHO, torque and moment of force are perfectly interchangeable, while word moment can be connected to several physical entities. Also, it seems that in anglo-saxon countries symbol $\vec{\tau}$ is prefered, while in the rest of world and according to ISO standard $\vec{M}$ should be used.
I would prefer that torque be used as well. Why is moment of inertia then not a cross product, if moment of force is a cross product? This is mathematically inconsistent. I was confused by the fact that the cross product of r and F (what is the cross product code?) is called torque in physics and moment of force in mechanical engineering, and that terminological inconsistency would interfere with at least my ability to understand the concepts behind torque. I will accept it if both physicists and engineers would agree on a single term for this concept, but I would prefer torque because calling both a cross product and a regular product a moment makes it unclear what a moment actually is, mathematically.
