Saturday, 6 May 2017

classical mechanics - Torque vs Moment


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.



Answer



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.


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