  After recalling the rigorous mathematical representations in Relativity
Theory (\emph{RT}) of (i): observers, (ii): reference frames fields, (iii):
their classifications, (iv) naturally adapted coordinate systems (\emph{nacs}%)
to a given reference frame, (v): synchronization procedure and some other key
concepts, we analyze three problems concerning experiments on rotating frames
which even now (after almost a century from the birth of \emph{RT}) are sources
of misunderstandings and misconceptions. The first problem, which serves to
illustrate the power of rigorous mathematical methods in \emph{RT}is the
explanation of the Sagnac effect (\emph{SE}). This presentation is opportune
because recently there are many non sequitur claims in the literature stating
that the \emph{SE} cannot be explained by \emph{SRT}, even disproving this
theory or that the explanation of the effect requires a new theory of
electrodynamics. The second example has to do with the measurement of the one
way velocity of light in rotating reference frames, a problem for which many
wrong statements appear in recent literature. The third problem has to do with
claims that only Lorentz like type transformations can be used between the
\emph{nacs}associated to a reference frame mathematically moddeling of a
rotating platform and the \emph{nacs} associated with a inertial frame (the
laboratory). Whe show that these claims are equivocated.
