Surmounting the Inherent Errors in the Trifilar Pendulum Measurement of Moment of Inertia

The trifilar pendulum is a comparatively simple apparatus for the measurement of the moment of inertia, but a thorough analysis of the many potential errors in such measurements does not exist in the literature. It typically consists of a circular platform suspended by three parallel cables attached equidistantly around a circle near the periphery of the platform. One measures the period of torsional oscillation of the pendulum empty and with the object in question centrally placed on the platform, and from a simple formula obtains the moment of inertia of the object about the axis of rotation. The published theory assumes that the object to be measured is placed on the platform with its mass center coincident with the mass and geometric centers of the platform. A detailed analysis of the error introduced by mass center offset is presented. All of the various measurements and pendulum properties are examined to evaluate the maximum possible total error. The final equation clearly shows the effect of the ratios of platform to object mass and moment of inertia. It is shown that period measurement is the most sensitive of the required measurements. An error estimation formula is given.