Abstract: As the major scale model test equipment in geotechnical engineering, the centrifuge has become more widely used in the fields of explosions and landslides involving high-speed movement of materials with the continuous improvement of its test capabilities. The general expression for the acceleration of matter motion in the moving reference system is strictly derived. Secondly, the governing equation for particle motion in the centrifuge model container is established based on the Newton's second law for centrifuges at a constant rotating speed. The relative motion of the particle is essentially related to three non-inertial actions, including uniform centrifugal force, non-uniform centrifugal force and Coriolis force. The non-inertial effects on the relative motion of particles caused by the three non-inertial actions are studied, and the sensitivity of the factors such as the initial coordinates and the initial speed is quantitatively analyzed based on the analytical solution. It is shown that the coupling of the three non-inertial effects affects the governing equation for the relative motion of particles, which makes it impossible for the law of similarity in the conventional model tests to be established accurately. The influences of the Coriolis force on the non-inertial effects are generally greater than those of the non-uniform centrifugal force. The non-inertial effects on free-moving particles are significant, but the particle motion component parallel to the centrifuge axis is not affected by the non-inertial system effects.