The spin inertia measurement is a recently emerged tool to study slow spin dynamics, which is based on the excitation of the system by a train of circularly polarized pulses with alternating helicity. Motivated by the experimental results reported by Zhukov et al. [Phys. Rev. B 98, 121304(R) (2018)10.1103/PhysRevB.98.121304], we develop the general theory of spin inertia of localized charge carriers. We demonstrate that the spin inertia measurement in longitudinal magnetic field allows one to determine the parameters of the spin dynamics of resident charge carriers and of photoexcited trions, such as the spin relaxation times, longitudinal g factors, parameters of hyperfine interaction, and nuclear spin correlation times.