Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: AndyJohnDOU on 07/05/2014 02:42:00
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hi
the direction of torque is defined by the i x j = k (cross-product right hand rule)
torque = ri x Fj
eg why is torque in the k direction and not in the -k direction?
is the torque direction calculated in the same way through-out the universe?
what factors determine that the torque is in the k direction and not the -k direction?
thanks
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If you apply a torque to something, you're going to tend to cause it to rotate about some axis. The most natural way to describe torque is by using that axis as a reference, i.e. having it point along that axis. And you're absolutely right about the ambiguity--should we have it point along the axis in one direction or the other?
We're actually free to choose as long as our equations work out correctly. But since physicists want to be as concise as possible and avoid confusion, they came up with a rule so that everyone uses the same convention, and this is the right hand rule. You could just as easily use the left-hand rule to flip the direction of torque and the same laws would hold.
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thanks for your response
I was happy with the i,j,k right hand rule that has been devised to explain how to determine which direction the torques would be in
sorry if I wasn't clear enough with my first question
what I wanted to know is what are the physical reasons that determine that torque is in the upward direction & not the downward direction in the example above
is it to do with the earth's rotation about it's axis, the rotation of the earth about the sun, gravity etc..
thanks
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There isn't a physical reason. That's what JP was saying. It is a convention that the torque direction is the way it is, but it is an arbitrary convention. If we used the opposite convention, the physics would be identical. There is no experiment to determine that the right hand rule it the correct way to describe torque and that the left hand rule is the wrong way. This is true of all quantities of angular motion (angular velocity, angular momentum, etc.) not just torque.
Take the example of the rotation of Earth. Viewed from above the North Pole, Earth is rotating in an anti-clockwise direction. Following the right hand rule, the angular momentum vector of Earth is pointed "north." If we used the left hand rule, we would just be describing the same rotation of Earth with a vector pointed in the opposite direction. Nothing physical changes, just the mathematical convention of how we describe the physical reality.
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thanks again
so there is no physical reason and the handedness is only due to the mathematical conventions we have chosen
and is arbitrary
I think I will go away and have another think about the physical meaning and about handedness and symmetries
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thanks again
so there is no physical reason and the handedness is only due to the mathematical conventions we have chosen
and is arbitrary
Exactly. For rigid rotation, what is physical is the axis of rotation and the way the object rotates about that axis. The fact that we choose torque to lie along the axis could be said to be relatively physical, since the axis is of physical importance. The fact that we choose it one way vs. the other is just arbitrary mathematical convention.