We will use the same numbers as the length of arm and wavelength in the textbook. Before and after the rotation, the time difference has the same amount, but the opposite sign. We are still able to see our face as usual. Our reference frame is inertial frame. We cannot distinguish which system is moving.
Force is proportionate to mass.
The form of law can be unchanged even though mass is different in different inertial frame. This is the second postulate of the special relativity. If the force is zero in one inertial frame, in any other inertial frame that must be zero. The order of the element in the periodic table is based on the number of electrons or protons in one atom. Even if two inertial frames have different orders, that is completely meaningless.