Mass Moment Determination Using Compound Pendulum

Abstract

This work has been performed to verify the existent knowledge on determination of the mass moment. For the experiment, a compound pendulum was used. The motivation to undertake these studies were experimental results indicating a big discrepancy in mass moments between the values coming from calculations using the definition formula and these obtained from the experiment. In relation to the axial moment the relative error equals 23.6 %, whereas regarding the polar moment the error reached 56.4 %. Considering the reason of that discrepancy we could find the existent theory not to be adequate. The theory is then considered in view of verifying first the mathematical pendulum and next the physical/ compound pendulum theory. The consideration has been focused on the description of accelerated motion cycle of both pendulums as it was enough to solve the problem. A source differential equation, which serves to solve any quantum phenomena, was used in the study. Then the course of creation of detailed characteristics of the phase of mathematical pendulum accelerated motion is presented as the basis to derive formula on the mass moment of a compound pendulum. At the end this new adequate theory was verified showing the relative error to be less than one per cent.