Understanding Moments: The Mysteries of Force and Distance Unraveled

[Noesis]

When trying to understand moments...two particular things bother me.

First Question

First...if the unit for moment is defined as a force x distance, a Newton-Meter perhaps, what the hell does that mean?

A Newton is very self explanatory...the amount of force needed to accelerate a kilogram of mass to 1 meter per second squared.

But a moment?

It seems as well that it would define some type of force about the axis of rotation...so why even have the meter there? It seems like the meter would just be a scaling factor, should be taken as being dimensionless, and a moment only defined in Newtons about a particular axis and direction?

Second Question

Why in the world do we use the cross product to define a moment vector? And why in the world do we want it to be perpendicular to ANYTHING?

If this is to facilitate our calculations...how are they facilitated? Could this be done differently?

I feel like a little monkey doing the homework problems...as I don't have a true understanding of the subject.

Thanks guys.

 

[Astronuc]

The moment causes something to bend or rotate. It is an action or force applied perpendicular to a moment arm or lever.

The units do seem a bit strange, but is does give the magnitude of force applied (perpendicularly) at a distance from some pivot or reference point. If the force is applied at an angle, it can then be resolved into perpendicular and parallel components with respect to the moment arm.

If the force were applied parallel, the arm would be under tension or compression.

 

[Noesis]

Thanks for the response Astronuc...glad I got you in here, I can pick an engineering heavyweight's brain, haha.

So the Newton-meter units do give the magnitude of the 'apparent' force applied let's say...why would we even have the meters in there?

It seems unnecessary. I mean, we really can't tell if a Newton-meter is 3 Newtons applied 2 meters away, or 2 Newtons applied 3 meters away, or any of an infinite combination anyway...why not do away with the meter part?

Or is there something I'm not thinking of?

How about the cross product/vector analysis that is done for them? That still puzzles me.

Thanks a lot Astronuc...I appreciate all of the help.

 

[berkeman]

The moment is a torque, not a force. Torque is the product of the force applied at the end of some lever arm, multiplied by the length of the lever arm. And you are correct, you get the same torque with half the force at twice the lever arm length -- it doesn't matter how the torque contributions ratio, as long as the product is the same.

Think about it. Given a particular arm strength and wrench handle length, which is easier to use on a pesky stuck bolt -- a wrench with a long handle, or one with a tiny short handle?

 

[Noesis]

Hey thanks a lot for the help Berkeman. Definitely the long handle, hah.

Ok..so the moment is a torque. What is the difference between a moment and a torque anyway?

A moment is the tendency of an object to rotate about a point...and a torque is simply the rotational force (defined as force times perpendcular distance) ? Or are they identical?

And actually..the same unit question would apply to torque. Why not get rid of the distance unit in the product since it only acts as a scaling factor? Maybe give it a different unit than a Newton since it implies rotation. Or is it necessary for some reason I don't know of?

About my second question...upon doing some work I realized the use of the cross product is because of it's definition as ABsin(x), it gives the magnitude of the force times the perpendicular distance...exactly what we want for torque/moment.

What I don't understand though is why do we have the direction of the moment vector be perpendicular to the plane that contains the force and the moment arm.

Why in the world do we do that?

 

[Astronuc]

Torque and moment are used interchangeably.

One uses r x F, where r is the position vector and F is the Force applied (usually normal) at distance r from axis of rotation. If the angle is 90°, the entire force is invested in the torque (sin 90° = sin pi/2 = 1).

IIRC, r x F, the resulting vector points in the direction that a right hand screw would 'advance' if subject to the moment or torque.

See -

http://www.netcomuk.co.uk/~jenolive/vect8.html

http://hyperphysics.phy-astr.gsu.edu/hbase/vctorq.html
http://hyperphysics.phy-astr.gsu.edu/hbase/torcon.html

http://physics.uwstout.edu/statstr/statics/StatI/stat131.htm

http://www.physics.uoguelph.ca/tutorials/torque/Q.torque.cross.html

http://omega.albany.edu:8008/calc3/cross-product-dir/cornell-lecture.html

 

[NotMrX]

Why in the world do we use the cross product to define a moment vector? And why in the world do we want it to be perpendicular to ANYTHING?

A plane in three dimensional space is most easily defined by a the line perpendicular to it. A plane contains many lines with many directions. The only unique direction is the line perpendicular to the plane. The two vectors that we cross for moment are in a plane, so the unique way to describe it is with the perpendicular vector.

 

[civil_dude]

One example of a force system that produces a moment is a couple.

A couple is two forces of the same magnitude but in opposite directions. Thus the object that the couple acts on will only rotate, no translate.

Now consider, as the distance between the two forces increase, what happens to the twisting "force" on the object? It has to increase. Now, to measure the twisting "force" or moment, we multiply the magnitude of the force times the PERPENDICULAR distance between them.

 

[Noesis]

Thanks a lot guys.

Those links and explanations were a great help in understanding what the hell is going on here.

Speaking of couples civil_dude...that's my next personal problem lol.

I'm about to open up another topic for that.

 

[Noesis]

Moment Couple Strangeness

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