PRINCIPLE OF OPERATION OF A MOMENT OF INERTIA INSTRUMENT

The moment of inertia of any object can be measured through its CG by hanging the object from a wire, twisting it slightly to initiate oscillation, and timing the period of oscillation. However, anyone who has ever tried this finds that the object swings from side to side and bounces up and down rather than rotating smoothly about an axis, making accurate data acquisition difficult. Furthermore, there are a number of practical problems involved in hanging most devices upside down. Where do you attach the wire? How do you hang the whole system? How do you calibrate the device, and what do you do to correct for the change in calibration when the weight of the test object stretches the wire?

Our instruments operate on the principle of the inverted torsion pendulum. Instead of hanging from a torsion rod or wire, the test object rests on a table attached to precision low friction bearings which constrain the motion of this torsion member to pure rotation. A sensing device produces timing pulses which start and stop a digital period counter to determine the period of the oscillating system.

The measurement of the moment of inertia of the test part is based on the change in the natural frequency of oscillation of the torsion pendulum resulting from the addition of the test part. This change in natural frequency is compared with the change in natural frequency which occurs when a calibration weight of known moment of inertia is placed on the instrument. These instruments are linear over a wide range of test part weight and moment of inertia. Instruments with measurement errors as small as 0.01% are available.

The test part is in motion during the measurement. It is essential that the part be rigidly located on the mounting plate of the instrument at the proper orientation. A variety of holding fixtures are available from Space Electronics, so that special test fixtures are rarely necessary.

Torsion Pendulum Theory