THE EFFECT OF MASS OF THREE-WIRE PENDULUM CYCLOID ON THE ACCURACY OF MEASURED MOMENT OF INERTIA

Using the three wire- pendulum to measure the moment of inertia is a common practice. The cycloid is usually assumed in an ideal state theoretically (i.e the mass of the cycloid approaches 0). But actually, if the workpiece measured is heavy, the mass of the cycloid can not be neglected, we have to consider the mass of the cycloid in the moment of inertia of the empty turning wheel. This paper uses the Halmiltonian theory and the variable substitution to derive the variable tension string vibration equation of the three wire-pendulum cycloid. And from the state of the point in the junction of the cycloid and the turning wheel (x=0), we obtain a computational formula for the moment of inertia by using the three wire-pendulum without neglecting the mass of the cycloid. In addition, we can make calculations by MATLAB.