The measurement of the full inertia tensor of a rigid body is a quite complex operation. It usually involves the measurement of different moments of inertia around different axes and then the reconstruction of the inertia tensor from these measurements. In the literature, many different test rigs developed for measuring the inertia tensor are presented. The problem of how locating at best the rotation axes to reconstruct the inertia tensor deserves still an in-depth theoretical study. In the paper the best way of locating such axes is studied and the results are compared with the most common combinations of axes used in the practice. The mathematical definition of the measurement accuracy of the full inertia tensor of a body is presented. The main sources of uncertainty are considered with the limitation that the centre of mass of the body under consideration lies on the axis of rotation. In the companion paper such a limitation is removed. The measurement accuracy of the inertia tensor can be substantially improved by redundant measurements. However such an approach has the drawback of making the measurement much more complex.
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