Why does torque depend on the perpendicular distance from the axis?

[paul-martin]

http://img113.exs.cx/img113/5240/Torque.jpg

 

[Doc Al]

I assume your diagram is meant to show the same force being applied to two different rods. What's different is not the force, but the torque that the force provides about the given axis. Loosely speaking, torque is a measure of the "twisting force" applied. The amount of torque that a given force produces depends not only on the force itself, but on the leverage of that force. Your second rod has the force applied twice as far from the axis, giving it twice the leverage and thus producing twice the torque.

 

[paul-martin]

Thx Al, but you didn't answer my question, you just gave a definition on what a torque is and who the distance from the rotation centre affect it's impact.

But my question was to understand why it is like that, why does the leverage affect how big the force is?

Thx for any answer given, kindly Paul-M

 

[paul-martin]

Also i can't find this topic i check the General Physics but doesn't se it so i go by my profil.

 

[T@P]

i have a 'guess' that might explain it: if you think of the massless rod as being the top of a right triangle (there's only one), then the longer the rod the longer the right part is. does that help? i mean you can reason that the force is cating away from the anchor point, and this anchor point has a harder time 'fighting back' if its farther away?

 

[paul-martin]

Seen I aren’t English is it a bit hard to understand what you are saying; to start with, what you mean with “being the top of a right triangle” also with anchor point do you mean the point the rod is trying to rotate around?. A picture would make it much easier to understand what you are trying to say.

Kindly Paul-M A

 

[T@P]

ill try with an ascii picture...

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so the top horizontal bar is the one you apply the torque too. from the diagram, if you think about it purely non mathimatically, the vertical bar of this triangle will be bigger if the horizontal one is, and then because i remembered that there vectors, you see that the force is bigger. sorry about the ishy explanation

*edit* sorry, i can't make the formatting changes stay. but if you imagine shifting the little slashes so that they form nice straight lines, i think you can get the idea