Measuring Mass Moment Of Inertia

Sometimes the shapes of machine parts are so complicated that it is extremely tedious and time-consuming to calculate the moment(s) of inertia. Consider, for example, the problem of finding the mass moment of inertia of an automobile body about a vertical axis through its center of mass. For such problems it is usually possible to determine the mass moment of inertia by observing the dynamic behaviour of the body to a known rotational disturbance.

The torsional stiffness is often known or can be computed from a knowledge of the length and the diameter of the rod or the wire and its material. Then the oscillation of the body can be observed and Eq. (16.4) used to compute the mass moment of inertia [G. Alternatively, when the torsional stiffness kt is unknown, a body with known mass moment of inertia [G can be mounted and Eq. (16.4) can be used to determine kt.

A trifilar pendulum, also called a three-string torsional pendulum, illustrated in Fig. 16.2, can provide a very accurate method of measuring mass moment of inertia. Three strings of equal length support a lightweight platform and are equally spaced about its center. A round platform serves just as well as the triangular one shown. The part whose mass moment of inertia is to be determined is carefully placed on the platform so that the center of mass of the object coincides with the platform center. The platform is then made to oscillate, and the number of oscillations is counted over a specified period of time.