THz radiation allows for the controlled excitation of vibrational modes in molecules and crystals. We show that the circular motion of ions introduces inertial effects on electrons. In analogy to the classical Coriolis and centrifugal forces, these effects are spin-rotation coupling, centrifugal field coupling, centrifugal spin-orbit coupling, and centrifugal redshift. Depending on the phonon decay, these effects persist for various picoseconds after excitation. Potential boosting of the effects would make it a promising platform for vibration-based control of localized quantum states or chemical reaction barriers.