  The concept of rigid reference frame and of constricted spatial metric, given
in the previous work [\emph{Class. Quantum Grav.} {\bf 21}, 3067,(2004)] are
here applied to some specific space-times: In particular, the rigid rotating
disc with constant angular velocity in Minkowski space-time is analyzed, a new
approach to the Ehrenfest paradox is given as well as a new explanation of the
Sagnac effect. Finally the anisotropy of the speed of light and its measurable
consequences in a reference frame co-moving with the Earth are discussed.
