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According to image a motor rotate two ring type flywheels(their mass concentrated away from center) one in clockwise other in anti-clockwise at high speed. If we try to change their rotation axis in same plane, would they try to oppose this change. In brief I want to ask- Is magnitude of force required to make this change is same or different when motor is on state(flywheels are running) and off state(flywheels are not running) ?

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The total angular momentum is zero, so no external torque is needed to get the axis to change. But there would need to be internal torques on both flywheels, it's just that each could provide the torque on the other. An external influence could then easily change the axis of the whole system.

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