Study of an adiabatic and free rotation of a block around a fixed axis using videoanalysis

Abstract

This work is a proposal for a basic physics class in which the statics and dynamics of a rigid body are approached simultaneously using a single experimental apparatus. A mechanical system was used to study the rotation of a rigid prismatic block around one of its edges. In the first part of this study (statics), the block is subjected to the action of a variable external force, the intensity of which decreases as the inclination of the block increases. The external force produces a slow rotation (adiabatic rotation) until it is in an unstable equilibrium configuration. The experiment allows data to be collected on the external force as a function of the block’s angle to the support surface. The graph of the theoretical force relative to the angle of the block with the surface is presented together with the experimental points. From the analytical expression of the force, the work is obtained and compared with the work of the weight force. In the graphical representation of work as a function of angle, a symmetry is identified in the curve drawings. In the second part (dynamics), the block is moved to rotate freely. The falling time is calculated considering two types of independent initial conditions. The first condition is a perturbation in angular velocity and the other in the initial angle. The graphs of the falling times as a function of the predicted perturbations are presented and the concordance between the experimental data and the respective theoretical curves can be checked. All equations obtained from the physical modelling are verified experimentally, through laboratory testing, image analysis and videoanalysis. The experimen-tal techniques and results are presented in detail throughout this paper. The practices described in this work are in harmony with active learning in physics teaching.