The uncertainty of the pendulum method for the determination of the moment of inertia

The purpose of this study was to quantify the uncertainty of the pendulum method for determining the moment of inertia of an object using various suspension distances. Experimental data were collected on a known geometric solid and partial differential equations were derived to calculate the uncertainty. Repeated measures were used to estimate the errors of the mass, period of oscillation, and distance measurements from the axis to the centre of mass. The results showed that the pendulum method was relatively insensitive to measurement errors of mass but was quite sensitive to errors in the period of oscillation. It was also found that the uncertainty of the pendulum method could be drastically reduced to less than 3% by suspending the object with the axis located at the radius of gyration. Most studies using the pendulum method to determine limb inertial properties have adopted a proximal suspension, including the often cited work by Dempster [Dempster WT. Space requirements for the seated operator. W ADC Technical Report 55–159. Ohio: Aero Medical Laboratory, Wright Air Development Centre, Air Research and Development Council, Wright-Patterson Air Force Base; 1955]. The results suggest that validation of imaging techniques to determine inertial properties should use geometric solids in addition to the pendulum method where the object is suspended at a distance estimated to be the radius of gyration. It is further recommended that the uncertainty be reported whenever it is necessary to use the pendulum method.