Using the “Moment of Inertia Method” to Determine Product of Inertia

Product of inertia is generally measured using a spin balance machine. In this type of machine, the object is rotated at a speed of about 100 RPM, and the reaction forces against the upper and lower spindle bearings are measured. Product of inertia is then calculated automatically by the machine’s on line computer, using formulas that involve the vertical spacing between the upper and lower bearings, and the height of the object above the mounting surface of the machine. Objects such as control fins and satellites with extended solar panels cannot be measured using this method, because of the large, non-repeatable errors which are introduced by the entrained and entrapped air and turbulence.

This paper outlines a method of determining product of inertia by making a series of moment of inertia measurements with the object-oriented in 6 different positions. Product of inertia can then be calculated using formulas which involve the rotation angles of the different fixture positions. Moment of inertia is measured by oscillating the object on a torsion pendulum. Since the object moves very slowly during this measurement, there are negligible centrifugal and windage forces exerted on the object. Furthermore, the mass of the entrapped and entrained air can be compensated for by making a second set of measurements in helium, and extrapolating the data to predict the mass properties in a vacuum.

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