I am a first year physics student and we recently learned about torque.
Every time I think I understand it something else comes up to confuse me - this time it is the direction. I tried looking in the forum and generally in google, but everyone only explains the right hand rule over and over again and that is not my problem. I will try to explain my difficulty as best as I can, I hope it will be clear.
I understand that cross products of 2 vectors give as a result a vector that is perpendicular to the plane of the two original vectors. I understand how to use the right hand rule and how to derive the direction of torque and I understand that mathematically it turns out to be perpendicular to the forces applied on the object.
My problem is that it doesn't make any sense logically to me that the direction of torque should be perpendicular to the plane created by the force applied to the object and the location relative to the axis it is being applied to.
##\tau = r × F##
The Attempt at a Solution
When I asked my lecturer she told me that the direction of torque basically represents whether the object is moving clockwise or anti-clockwise. So I understood that if the force was in the direction i and located on j then the torque is directed towards ixj=k and this k does not mean "the third dimension" or "pointing in or out of the page" but rather just "turning clockwise or anticlockwise" for -k or k. She said that it turns out it means both, or maybe I misunderstood her. This confused me even more.
Torque by definition is "tendency of a force to rotate an object about an axis, fulcrum, or pivot" (Wikipedia, I know, not the most trustworthy place, but good enough for my cause I think). By this definition I would expect that the direction for a torque for a given force would have to do with the direction of the force and the location relative to the axis (like it is) but remain on the plane they create.
So to conclude - why is the direction of torque perpendicular to the plane of the force and relative location from the axis that it is being applied to?
Sorry if it took me too long to explain, I hope it is clear enough, tell me if anything needs more explanation as to what my difficulty is.
Any help would be greatly appreciated.
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