Rotational Velocity: Force, Torque, & Axis Motion

[Del8]

Hi,

The green axis is fixed to the ground. An arm is turning clockwise at w1. The blue ring is turning at w2, with w2<w1. w1 and w2 are in labo frame reference. The ring is turning around itself counterclockwise at w2'=w2-w1, w2' is in arm frame reference. There is no friction.
http://imagizer.imageshack.us/v2/800x600q90/673/UPZdj7.png

I apply a force Fa on the arm with my hand. The axis of the ring receives Fb, for me w2' is constant because there is no torque on the ring. Is it correct ? If not where is the torque for change w2' ?

 

[voko]

Your idea that angular velocity of a rigid body is frame-specific is false. It is frame-independent and invariant. What you denote $\omega_2'$ is not angular velocity and it need not have any 'torque' related to it.