Experimental Measurement of the Inertia Tensor

The implementation of a simple torsion pendulum is presented in order to obtain the inertia parameters of an irregular-shaped body. The system consists of a fixed frame and an inertial frame which is attached by two strings to the fixed frame. The idea of the torsional pendulum is proposed in the book “Lagrangian Dynamics” [1], following the idea presented in it an apparatus was created in order to measure the inertial moments of an aquatic vehicle along its yaw axis of symmetry. In order to make said measurements it is necessary to determine the torsion constant of the string used, steel caliber 12, and the inertial moment of the inertial frame for which two measurements were made using a homogeneous body whose inertia moments where known (homogeneous aluminum cylinder). For calibration purposes the equation for the inertia moments was obtained for a sphere composed of two different materials (basketball), using said expression theoretical calculations were made and the apparatus was used to experimentally measure the moments of inertia, the results compared were found to be similar. Finally, the yaw moment of inertia for the mini submarine was measured.