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There's a PDF attached to this; have I concluded things the right way?
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Yeah I was thinking about that, but it's just a distance...I mean, its just the magnitude of displacement...it's like taking a measured section of a scale...that doesn't have a direction.The torque is dependent upon the direction of the lever arm and the direction of the force, so you can't neglect sign or direction (the latter is what you have neglected).
Humm...so actually it is relative. Its for me that the direction is changing...as a result I'm taking it as the modulus.The reason why the torque is in the same direction for both is because you are applying the force in the same direction with relation to the lever arm.
What is just a distance? There are two interesting vectors in your picture. The first is the vector from the fulcrum/pivot to the point where the force is applied to the beam. (If we conveniently chose the fulcrum to be the origin of our coordinate system, then that vector would just be the position vector of the point on the beam that's getting pushed. But regardless of the coordinate system we choose, it's still a vector.)Yeah I was thinking about that, but it's just a distance...I mean, its just a displacement...it's like taking a measured section of a scale...that doesn't have a direction.