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The question is: how to determine the axis and direction of rotation of the ideal non-metallic ball, which is in vacuum and weightlessness, without disturbing its state.
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Light it with a laser and measure the change in the wavelength of the reflected light along the edges of the visible disk - on one side it will be in the red side (here the surface is removed), on the other - in the purple (here the surface is approaching). The Doppler Effect. The location of the "red" and "violet" zones will show the axis, and the amount of shift is the speed of rotation.