why is angular velocity a pseudo vector but angular frequency a scalar

Question

I note that angular velocity is a pseudo vector as direction is only either clockwise or anticlockwise. So 'I believe ?' that the direction is given by the sign, so a positive value defines an anticlockwise rotation and negative value a clockwise rotation.

We say angular frequency is a scalar and it has the magnitude of the angular velocity. But if I put a positive sign in front of an angular frequency it is defined as anticlockwise rotation and similarly a negative is a clockwise rotation.

So from above I think both look like pseudo vectors ?

Note I come from electrical eng background so maybe these conventions are associated only with EE.

Answer 1

Angular velocity is the cross-product of two true vectors, position and velocity, as such it behaves like a vector under rotations but does not reverse under reflections so fails to be a true vector. Neither reflections nor rotations have any effect on angular frequency, so it is a scalar.

Answer 2

I do not actually view angular velocity as a pseudo vector. Its direction is given by the right-hand rule, the same as angular momentum. It is a full vector. The angular frequency, as you say, is the magnitude of the angular velocity, and is hence a scalar. It has no direction. I would not refer to a negative angular frequency, although perhaps some authors do.

Answer 3

Thanks for response. I did a little reading and what I was missing is that the velocity vector points perpendicular to the plane of motion so velocity vector has infinite number of directions like any other vector but is still psedo as its reflective symmetry is different from normal vectors. The angular frequency is scalar as we loose the plane of motion as all we are interested in is the frequency (the frequency is independent of the plane of motion) . I was mixing up the direction of rotation with the direction of the velocity vector (thety are different things).