The Mathematica notebook applies the equation of a physical pendulum and the conservation of angular momentum to study advantages and disadvantages, mainly related to safety (Figure 1), between statically balanced and unbalanced mechanical structures of different gantries. Furthermore, a trapezoidal equation of motion has been applied to model the rotation of different scenarios of gantry in nominal conditions. The notebook can calculate the ideal energy needed for a given operation (rotation of 180°) subdivided in equal angle steps, that is a simplification of treatment delivery operation by means of a gantry. The Energy used during operation is compared between scenarios (Figure 4). The ".pdf " version is also available.