  Employing a relativistic rotational transformation to study and analyze
rotational phenomena, instead of the rotational transformations based on
consecutive Lorentz transformations and Fermi coordinates, leads to different
predictions. In this article, after a comparative study between Fermi metric of
a uniformly rotating eccentric observer and the spacetime metric in the same
observer's frame obtained through the modified Franklin transformation, we
consider rotational phenomena including transverse Doppler effect and Sagnac
effect in both formalisms and compare their predictions. We also discuss length
measurements in the two formalisms.
