The centre of mass of a 'flying' body revealed by a computational model

The interpretation of complex trajectories of rigid bodies by the identification of their centre of mass (CM), has a large potential for improving the understanding of the concept of CM at college and university level. Therefore, it is not surprising that there are several techniques described in the literature concerning how to identify the CM of rigid bodies. However, these techniques fail when the CM's position in the body's frame of reference changes when the body is at motion. In this work we present a computational model that allows the identification of the CM with very good accuracy, either when the CM's position changes or is fixed in the body's frame of reference. This model can be used for a system of bodies moving in a plane, for which the CM of each body coincides with its geometric centre. The effectiveness of this model is tested with experiments using video acquisition and numerical analysis, and can be done in experimental classes under controlled conditions. Students are then able to compare the computed CM with the experimental CM, and investigate why the bodies sometimes present weird trajectories. This property applies in particular to sports, so the model can be also very useful as an educational resource for the explanation of the motion of athletes, namely as a tool for optimizing their performance.