Rotational Velocity: Force, Torque, & Axis Motion

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The discussion centers on the dynamics of a rotating arm and a ring, focusing on angular velocities and the concept of torque. The arm rotates clockwise at a speed w1, while the ring rotates counterclockwise at a speed w2', which is derived from the difference between w2 and w1. A force Fa is applied to the arm, and it is stated that the ring's angular velocity w2' remains constant due to the absence of torque. The conversation challenges the notion that angular velocity is frame-specific, asserting that it is actually frame-independent and invariant. The key question raised is about the existence of torque affecting the change in w2'.
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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' ?
 
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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.
 

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