Antony Marco Mota Polito

Dinâmica de corpos rígidos em superfícies com atrito

In this work, we present the theoretical and experimental treatment of the motion of a disc supported by four points lying on a horizontal surface with friction. The mathematical solution of this problem was obtained in the context of the lagrangian formalism. Unlike the case of smooth surfaces, we need add to the dynamical equations the generalized forces that couple the dynamics of translation of the center of mass and the dynamics of rotation around it. Due to the complexity of the equations, numerical solutions are required. The numerical solution allows both to obtain the trajectory of the disc and to observe the effects of the coupling in the decays of the rotational and translational mechanical energies. Seeking for reproduce the calculated dynamics an experimental device was idealized and effectively build. Beyond to reproduce qualitatively the predicted effects, the device was also utilized to implement a pedagogical sequence in order to present the concepts of mechanical energy (potential and kinetic), its transformations and its irreversible loss by dissipation, in a depth adequate for a first year high school class.