Angular Velocity: What's the Difference between Horizontal and Vertical Circles?

[Air]

Can someone please explain the difference in Angular Velocity for a Horizontal and a Vertical circle?

 

[CompuChip]

If you view it as a scalar quantity, there is none. Just by relabeling the x, y and z axis you can always get the circle to lie in the (x, y) plane and make it "horizontal". If you view the angular velocity as a vector, the difference will be that it points along one axis ("z") in one case and along another (e.g. "x") in the other.

So what exactly do you mean by "horizontal" and "vertical" circle, how do you define angular velocity and how would it be different?

 

[Air]

I'm thinking of it in terms of conservation of energy. I believe Motion in a vertical circle, conservation of energy applies. In a horizontal v=(omega)r and omega is constant.

Can anyone explain this theory further?