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A balanced wheel has two large masses attached to the rim opposite each other with respect to the axis of the wheel. The wheel is spun up to high speed but remains balanced to an inertial observer at rest with the non spinning axle of the wheel.

To an observer in an inertial reference frame that has velocity relative to the axle of the wheel, the wheel appears to be elliptically shaped. The two masses are opposite each other when both masses are exactly orthogonal to the linear motion of the wheel. Call those positions 12 O'clock and 6 O'clock. When the rim masses are at 9 O'oclock and 3 O'clock simultaneously in the rest frame they are somewhere near 10 O'clock and 2 O'clock in the moving frame. It is obvious that the centre of mass of the wheel in the moving frame is not in the centre of the wheel and that is a fairly well known fact of relativity. What is puzzling is that the centre of mass is constantly moving as the wheel rotates in the moving frame so superficially it seems impossible for the wheel to be balanced in the moving frame and should oscillate up and down.

Is this an example of De Broglies hypothesis that a particle with linear motion has a characteristic wavelength?

Is the assumed "wobble" corrected by the fact that the acceleration vector is not always parallel to the the vector of the force causing it in relativity?

Is the assumed "wobble" corrected by stress in the spokes being an effective mass according to the stress energy tensor?