Confusion about adding angular velocities

[Bastian1978]

TL;DR

I'm confused about how adding angular velocities works, in an example situation.

I'm trying to learn about adding angular velocities, and I'm confused about something. In this diagram...
https://i.sstatic.net/S6C03.png
there is a large orange disc rotating with angular velocity A (relative to the ground), and attached to the large orange disc is a small green disc, which is rotating at angular velocity B (relative to the large orange disc).
My understanding is that if I want to calculate the angular velocity of the small green disc, relative to the ground, then I would add A and B.
In the example I'm imagining, A is rotating anticlockwise at 1 radian per second, and B is rotating clockwise at 1 radian per second. So if I add A and B, I would get zero. I think that makes sense, since it'd mean that the orientation of the small green disc isn't changing relative to the ground.
The part that confuses me is that even though the orientation of the small green disc isn't changing relative to the ground (because its angular velocity relative to the ground is zero), if we imagine a point on the ground positioned at the centre of the large orange disc, the small green disc would be orbiting that point. So I don't understand how the green disc can be orbiting a point and yet have an angular velocity of zero?
I think I'm misunderstanding something fundamental about this, so if anyone could help me understand it better, that'd be great.
Also, I'd really appreciate being pointed to some reference material about this, particularly about how addition of angular velocity vectors works.
Thanks!

 

[Baluncore]

In the example I'm imagining, A is rotating anticlockwise at 1 radian per second, and B is rotating clockwise at 1 radian per second. So if I add A and B, I would get zero. I think that makes sense, since it'd mean that the orientation of the small green disc isn't changing relative to the ground.

If fixed to an orbiting disc that is not rotating, the ground directions do not change, north is always in the same direction.

In the diagram they are both rotating anticlockwise, the sum is 2 radians/sec.

 

[A.T.]

So I don't understand how the green disc can be orbiting a point and yet have an angular velocity of zero?

https://en.wikipedia.org/wiki/Angular_velocity

There are two types of angular velocity:

• Orbital angular velocity refers to how fast a point object revolves about a fixed origin, i.e. the time rate of change of its angular position relative to the origin.
• Spin angular velocity refers to how fast a rigid body rotates with respect to its center of rotation and is independent of the choice of origin, in contrast to orbital angular velocity.

 

[Lnewqban]

You could also pay attention only to the relative rotation of the small green disc and the shaft that holds it.
That would remove the confusing orbit trajectory of that shaft (about which the small green disc "knows" nothing).

That shaft would be fixed or would rotate with angular velocity A relative to the ground.
Any other translational movement of the shaft would not be relevant to that green disc-shaft relative rotation.

 

[Bastian1978]

Thanks for your replies.
So is it correct to say that in rigid body dynamics, such as in Euler's equations of motion (https://en.wikipedia.org/wiki/Euler's_equations_(rigid_body_dynamics)) we're only concerned with the "spin angular velocity"?