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Question:
Why does a gyroscope all the crazy things it does? At least to me they seem crazy because I have no idea where the forces causing all that come from. My teacher tried to describe it to me, and told me vectors causing everything, but I didn't understand it. It made no since to me to have a vector that is pointed perpendicular to its component vectors. I hope you can help me ,and give me an explanation that I can understand.



Replies:
Well, angular momentum is DEFINED by a vector cross product, which always produces a resultant vector that is perpendicular to the two vectors you are taking a product of. In fact, one way to think about a cross product is that the magnitude is equal to the area of the parallelogram formed by the original vectors, and the direction is perpendicular to that parallelogram - the cross product describes that particular parallelogram (its area and orientation at least). But that does not exactly explain what it has to do with rotation of a gyroscope... Actually, if we lived in any dimension other than 3, angular momentum would not be a vector at all, but would be an antisymmetric second-rank tensor - if that helps! So, to some extent it is a little coincidental, and you have to try and understand the math behind it, or else just accept it on faith that this vector along the axis of rotation has these particular conservation properties that follow from conservation of momentum. Once you accept that (or understand it) then the properties of the gyroscope are not that mysterious - it is only changing this vector when some kind of force is applied just like with regular momentum, except that the "angular force" (or torque) is also obtained by this cross product rule, and so is perpendicular to the axis and the vertical direction (in the case of gravity) and with the torque always perpendicular to the angular momentum you get a kind of circular motion...

Arthur Smith



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