What simple concept am I missing about moments?

[mindheavy]

In a two-dimensional statics problem involving finding a moment about a point, I don't understand how the result is either in the positive/negative z direction.

I realize moments are found by the cross product, and the cross product requires the answer to be perpendicular to the plane that the two vectors form.

If I look down at the surface of my desk and take that to be an x-y plane. a pencil laying on the plane is held stationary at it's left end, and the right end is made to rotate clockwise. This tells me that I can expect my moment to be in the negative z direction (say, going down through the surface of the desk). This makes no sense to me, what concept am I missing here?

 

[tiny-tim]

hi mindheavy!

it's a convention

we could define it other way round (ie moment up for clockwise)

(like we could say electrons have positive charge, protons have negative charge)

but we don't, we say moment down for clockwise, moment up for anti-clockwise

what don't you like about that? ​

 

[mindheavy]

What I don't like is thinking of the pen rotating clockwise and knowing that the 'answer' for the moment is going down through the desk. Is it that I don't really get what a moment is? It's easy for me to understand that a force applied to the pen causes it to rotate, but why is the moment saying the result is perpendicular? Why is the result not just the direction of rotation?

Another way I'm looking at it:
I'm imagining standing at a slot machine, the lever is directly in front of me. When I pull this lever down, there's a force acting on it going straight out either left or right? This makes no sense to me.

 

[tiny-tim]

hi mindheavy!

I'm imagining standing at a slot machine, the lever is directly in front of me. When I pull this lever down, there's a force acting on it going straight out either left or right? This makes no sense to me.

it's not a force

(it's not even a vector, it's a pseudovector)

it's a moment (or torque or couple)

imagine that lever is twice as long, with the pivot in the middle

you'd produce the same effect by pulling one end down and the other end up

the total force is zero

only the total moment is non-zero

What I don't like is thinking of the pen rotating clockwise and knowing that the 'answer' for the moment is going down through the desk. Is it that I don't really get what a moment is? It's easy for me to understand that a force applied to the pen causes it to rotate, but why is the moment saying the result is perpendicular? Why is the result not just the direction of rotation?

but the direction of rotation is perpendicular to the desk!

here's a question for you:

how would you describe the direction of rotation of the earth?


(and if you wanted to make the Earth rotate faster, what would you call the direction of the moment you should apply?)​

 

[mindheavy]

Ok, this is starting to become clearer. Getting a vector when calculating a moment made me think of a force, but if it isn't actually a force, it will be easier to grasp.

I would describe the Earth as rotating about it's vertical axis, and the direction of this rotation is perpendicular to that axis.

Is that a main idea here, being perpendicular to the axis?

 

[tiny-tim]

I would describe the Earth as rotating about it's vertical axis, and the direction of this rotation is perpendicular to that axis.

Is that a main idea here, being perpendicular to the axis?

nooo, the direction of rotation is the axis

that's the only way we can unambiguously define rotation!

the Earth's axis is N-S

perpendicular would be any diameter through the equator, but which one? through ecuador? through kenya?

isn't the only sensible direction of rotation the line through the poles? ​

 

[mindheavy]

I thought it would be the line perpendicular to the axis of rotation, at any point along that axis, maybe I have some more reading to do :)

 

[timthereaper]

A vector is really just a magnitude and a direction. When vector analysis was developed, someone thought, "Hey, we can apply this to physics!". Forces have a magnitude and a direction, positions can have a magnitude and a direction from an origin, so using vector-based math seemed like a perfect fit.

Some scientists figured out that if you do the vector cross product of a (relative) position and a force, you get a vector whose magnitude corresponded exactly to the magnitude of a moment created around a point. The direction of that vector is a result of the cross product operation (following the right-hand rule). In vector analysis, that cross product vector is perpendicular to the plane that the two original vectors lie in. Translating that into the physical problem, they determined that the direction pointed along the axis of rotation and perpendicular to the plane of the created moment. They also figured out that which way the direction vector pointed identified which way the moment "spins" on that axis.

The moment vector is still just a magnitude and direction, but it tells you in what plane the actual "rotation" occurs, which way it's "spinning", and what the magnitude of the moment is.