ABSTRACT
To analyze the accelerations of geared systems, it is necessary to determine their effective moment of inertia. The inertia force can be reduced to zero if adjustments can be made to the rotating system so that the center of mass of the system lies on its axis of rotation. It should be noted that the inertia force introduced is proportional to the square of the angular velocity, and for high-speed machinery, this inertia force can be very much greater than the weight of the mass. The center of mass of a system may not be on the axis of rotation due to the geometry of the system or due to the lack of homogeneity in the material. A vibrational or oscillatory motion of a body is referred to as force-free or natural when the body is acted upon only by the restoring force arising from its displacement.
