  In this work we introduce two experimental proposals that could shed some
light upon the inertial properties of intrinsic spin. In particular we will
analyze the role that the gravitomagnetic field of the Earth could have on a
quantum system with spin 1/2. We will deduce the expression for Rabi
transitions, which depend, explicitly, on the coupling between the spin of the
quantum system and the gravitomagnetic field of the Earth. Afterwards, the
continuous measurement of the energy of the spin 1/2 system is considered, and
an expression for the emerging quantum Zeno effect is obtained. Thus, it will
be proved that gravitomagnetism, in connection with spin 1/2 systems, could
induce not only Rabi transitions but also a quantum Zeno effect.
