Vector representation of angular quantities?

Question

In the world of pure rotation, a vector defines an axis of rotation, not a direction in which something moves. Does it means that angular quantities like angular momentum, angular speed, torque etc all are represented in vector form in same direction i.e along the axis of rotation ? Or there can be some cases in which they are in different directions w.r.t each other ?

Answer 1

To record ACuriousMind's comment:

Many "angular quantities" are actually pseudovectors rather than vectors, for the difference, see this question.

Actually, he's being too modest: go straight to his answer to the question "When is it useful to distinguish between vectors and pseudovectors in experimental & theoretical physics?".

The only thing that I would add to it in the case of rotations is that the angular momentum and angular velocity are in general in different directions (or, more precisely, they are different hyperplanes). The inertia tensor relates them. In the axis picture, the inertia tensor is a matrix that takes as input the angular velocity and outputs the angular momentum - in general this is a different vector direction. Axes of rotational symmetry of an object are eigenvectors of the inertia tensor, so, for example, if a cylinder rotates about its axis of symmetry, the angular velocity is in the same direction as the angular momentum. But this is not generally true.

Naturally, also, as things arising from external, causative agents acting on a body, torques can be in arbitrary directions relative to a body's angular momentum, the former being proportional to the time derivative of the latter, through Euler's second law.