Could anyone please explain to me what "moment" is?

Question

We have certain Physical quantities called "moments", like Moment of Inertia, Moment of Torque, etc. What exactly is this single term "moment"? Now, I'm not asking for a mere Mathematical equation finding the use of this term in it, nor do I ask for the meaning of "Moment of Inertia" or "Moment of Torque" separately. I want to know the exact definition of the single term "moment" only; I don't want to know what, say, "Moment of SOMETHING" means, for the time being. I have head-banged over this question for over a year now, searched books & libraries, asked friends & teachers, and the answer still seems to be far from reach. Please help me out. Thank you.

Answer 1

force *distance=moment

say in one end of a stick an weight  10 kg is hanging and length is 12 metre

then moment of this force is

10*12=120 kgmetre

see and refer

http://en.wikipedia.org/wiki/Moment_(phy...

Answer 2

I asked the same question for years.. ..here is what ive come up with.  From my recollection.  It is a quantity that represents the magnitude and direction of the SOURCE of a field (vector quantity).  Of course "Field" in this sense could mean what you normally would think of as a field ...electric, magnetic, gravitational.   Dealing with fields are easier for me...the other half of the confusing story deals with rotation.  In terms of rotation you will need a term to describe the source of the rotation (axis) the magnitude, and the direction (In physics direction of surfaces are perpendicular) ...hmmmm, might as well use the term "moment" because of the similarity with the definition when relating to fields.     Hoped that helped.

Answer 3

I've never heard of "moment of torque."  Sounds like it would basically mean "moment of inertia," since that is simply the resistance of an object to angular force--i.e., torque.

Be that as it may, moment, as it is used in physics, basically means inertia, but in response to various forces and force-related actions.  That is, how much resistance does an object put up, in response to various applied actions?

The analogue in linear dynamics is simply mass.  The more mass an object has, the more applied force is needed to produce a given acceleration.  Similarly, the more moment of inertia an object has, the more applied torque is needed to produce a given angular acceleration.  And the greater the dipole moment on a given dipole, the more electromagnetic impulse is required to manipulate the dipole.  And so on.

EDIT: I should add that there is a related notion of moment, in statistics, that occasionally comes into play in physics.  The so-called "first moment" of a quantity is its average.  This makes sense with moment of inertia, which is basically a measure of how far the average piece of an object is from the axis of revolution, multiplied by the average density of that object.

This correspondence extends further, too: For the purposes of an applied linear force, you can often treat an object as though it were all concentrated at a single point, located at the "average position" of the object (its centroid, if you care to look that up).  In the same way, for the purposes of an applied angular force, you can often treat a revolving object as though it were all concentrated at a single point (like a yo-yo, swung around in a circle), located at an average distance from the axis of revolution.

There is also a quantity's second moment, which is the average of the quantity's square; the third moment, which is the average of the quantity's cube; and so forth.  These all have some significance in statistics, and therefore the statistical aspects of physics (such as thermodynamics), but they start to stray away from the original physical notion of moment as a kind of inertia.

Answer 4

Good question

How about effective leverage? Or effective resistance to torsion/bending/deformation/rotation?

By the way I never could get to terms with the units of the moment of area of a rectangular section 1/12 b*d^3 (it is a bit mind-boggling to imagine a fourth power space dimension - Meters^4)

Answer 5

moment is the product of a force and a distance, where the distance is perpendicular to the force.  It is therefore  a torque as you would apply for example to a wrench

Answer 6

Okay, here's what a moment means in general:

A moment of X about some point is the sum (if X has a discrete distribution) or integral (if X has a continuous distribution) of X(as a function of position) times the displacement from your point to that position over all space.  Because displacement is a vector, a moment is a vector.

Some examples:

Moment of mass (the real honest-to-god, mathematical moment of inertia--not the thing we call moment of inertia) is the sum/integral of mass times displacement.  When you divide the moment of mass by the mass, you get the center of mass.

Moment of force (which engineers just call moment and physicists call torque) is the sum/integral of force times distance.  To be precise, the moment of a vector is the cross product of the vector and the displacement.

An electric dipole moment is the sum of charge times displacement.

Because there's no such thing (that we've found yet) as magnetic charge, a magnetic moment is a bit more complicated (since it's generated by loops of moving electrical charge.  But if there were such a thing as magnetic charge, the magnetic moment would be the sum of magnetic charge times displacement.

Now moment of inertia is unfortunately named, because it is the SECOND moment of mass, not really the moment of mass which I described above.  We ought to call it second moment of inertia.  The second moment of X about a point is the sum/integral of X times the SQUARE of the distance to the point.  So moment of inertia is the sum/integral of mass times the square of the distance to the axis of rotation.

Second moment of area shows up in engineering from time to time--the sum/integral of area times distance squared.

If you want to understand generally what a moment is, do not look at the wiki link above to moment (physics), which just describes moment of force/torque.  That article is misleading, because when a physicist says moment, that's usually not what he or she means. If he means moment of force, he'll say that or say torque.  Somebody should really improve that article to encompass the different moments used in physics.  Look at moment (mathematics) for a better definition of what a moment it (but unfortunately no physics examples)

http://en.wikipedia.org/wiki/Moment_%28m...

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I don't think anyone is really going to give you what you're looking for.  Maybe an analogy will help explain why.  Let's say I made up some term to descibe a time derivative.  I'll call it Q.  From now on, velocity is to be known as the Q of displacement.  A mass flow rate is Q of mass.  Current is Q of charge.  Now someone asks me to describe what Q feels like without the mathematical formulation, without just saying that a Q is a time rate of change.  It's tough, because all the different Qs "feel" a little different.  And I've also got double-Qs.  Acceleration is the QQ of displacement.  The voltage across an inductor is the QQ of charge.  And these are even more abstract and more different from each other.  Now add the fact that at some point, I got lazy and accidentally called acceleration the Q of displacement instead of the QQ.  And the name stuck and it won't go away.  So people want to intuitively compare it to the other single Qs.  See the issue?  The best thing I could do is give lots of examples and show how the Qs show up together in equations:

mass flow rate= velocity * linear mass density

Q of mass = Q of displacement * linear mass density

Q of current = Q of displacement * linear charge density

Likewise, the E&M moments coupled to E&M fields give us torques.

Moment of mass about a point * g = gravitational torque about that point.

So a moment of something tells us a combination of how much and how far away.  And that's about as good as I can do.  What the something is effects how the moment feels.

And the second and higher moments are even tougher to grasp except as mathematical constructs.