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.
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...
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Update: June 2012