Does "moment" have a single meaning in physics?

Question

I am a high school student and I am curious about the word moment and what it means in different contexts, whether it has a definite meaning or not?

I know it has some relation to different kinds of motion, like linear momentum (measures the "amount of motion" in a rectilinear path) or angular momentum (circular or hyperbolic path).

But I have difficulty in understanding how it relates in vector quantities like Dipole Moment, or moment of Inertia (Scalar quantity) or Magnetic Moment, or any other terminology that I haven't yet encountered.

Would help if someone brought some light to it. I appreciate all answers.

Answer 1

The basic meaning of the latin word "momentum" is movement or the power to move. The specific use of the term to mean mass $\times$ velocity was a comparatively late (seventeenth century) development.

But "moment", the anglicised version of the word, had already gone into speech to mean the power to get things going in the sense of importance or consequence; Shakespeare's Hamlet talks about "enterprises of great pith and moment". The word is still occasionally used in this sense in everyday speech, and we have the adjective "momentous".

So the turning moment of a force is the force's ability to turn things. Multiplying the force by the perpendicular distance from a point is what measures the force's ability to do this, its consequence, indeed its moment!

I suspect that using the term "moment" when we multiply of a quantity by a significant distance, as when we calculate the electric dipole moment of a collection of charges as $\sum Q \vec r$, is modelled on the calculation of the moment of a force (or the combined moment of a number of forces). Indeed 'moment' has pretty much taken on the meaning of a quantity multiplied by in some way by a distance or displacement from an axis or from a point, but the basic idea of giving importance to the quantity (in a particular context) by so doing is still in the background.

And what about the moment of inertia of a rigid body? To calculate this we multiply each mass element by a distance squared, rather than by a distance, before summing. But again we are constructing from the masses a quantity of moment when it comes to rotation. To be more specific, multiplying by $r^2$ gives us what is now called the second moment of mass, the first moment being multiplication of each mass element by its distance from an axis before summing (and quite likely dividing by the total mass in order to find the position of the centre of mass). The zeroth moment, $\sum m r^0$, is the simple sum of masses, but this is no doubt a later extrapolation from the original terminology.

This answer probably seems rather hand-wavy, but don't forget that it is only names that we are talking about. We could call the moment of inertia "Charlie" and it wouldn't affect the Physics. Names of quantities in Physics are usually very logical and helpful, but not always, as in the case of electromotive force. Moment is not quite in this category, but it's possibly not the most transparent of terms.

Answer 2

You might be interested in the etymology of the actual word moment.

See https://en.wiktionary.org/wiki/moment#Etymology

I'm no expert but that's how I think about it: All those different kind of moments basically describe a motion. A motion is basically the change of position. Now in a fixed amount of time, all those particles and charges and what not change their position differently. The only "constant" (not literally) is the fixed amount of time => a moment. In a given moment, the considered physical body moved such and such.

So you call it a moment.

Now again, I'm by far an expert and with the statement above there might be something wrong. Don't overthink it. I really like to try to understand the origin and etymology of a word, it might give you some small insight.

In future, just google the word and etymology or look for an etymology entry in the wiki. You could also search which person "invented" whatever you are researching and check in which language he/she wrote the paper. Maybe it's German or French or Latin, so you could check if that word has a meaning in those languages. E.g. moment is very common in German.

A great example from math is "Eigenvector, Eigenvalue". The word "Eigen" means "own" in the sense of "myself". (terrible translation) Which makes sense because an Eigenvektor is kind of invariant, it doesn't change. It's "true to its own" or however one would put it in English. :)

So don't overthink it. I always loved having a historical context to what I'm learning since it put it in perspective, so I get why you like to know why we call something.

As far as I know the connection between all those moments is more philosophical than anything else. (I might be wrong though! Maybe we can get all of those out of some theory. I'm still a noob myself.)