I just don't get this whole right hand rule thing. If you have a rotating disk, how the heck can its momentum vector product point perpendicular to the disk?! There is absolutely no motion perpendicular to the disk.
Why wouldn't it!
Like the others said, if a disk is spinning in the x-y plane, there's no motion in the x or y direction either. Which way would you have the vector point?
The only thing that makes sense is to have the vector point in some direction with circular symmetry. Why? Because if we rotate in the x-y plane a disk spinning in the x-y plane, the result is a disk spinning in the x-y plane, and the same vector should represent both situations. The only choice is to have a vector that points along the z axis!
A more thorough answer is that angular momentum is really a
bivector. An ordinary vector is, heuristically, a line element that points in a 1 dimensional direction. A bivector is a plane element that points in a 2 dimensional direction. The angular momentum of the aforementioned disk should really be written as a real multiple of
i^
j where ^ means wedge product. (it "pastes" lower dimensional vectors together to form higher dimensional vectors; here it combines a vector pointing along x with a vector pointing along y to form a bivector pointing along the x-y plane)
However, any geometrical object has a dual representation. Instead of a generalized vector that points in the direction the object is going, we can write a generalized vector that points in the direction the object is
not going. In particular, in 3-D geometry, any surface can be completely characterized by its normal lines, e.g. the dual to a bivector is its normal vector.
So, we use this dual vector to represent angular momentum because it's just an ordinary vector, which means we don't have to take a course in Grassman Algebra or Tensor Analysis to understand what it is.
Hurkyl