HOME EXPERIMENT TO CHECK THE RATIO OF THE COMPONENTS OF THE INERTIA TENSOR OF A THIN PLATE

Abstract

Formulation of the problem. One of the most difficult concepts for first-year students of a technical university, when studying the topic "Ridged body dynamics " in the physics course, is the concept of the moment of inertia tensor. The experimental determination of the components of this tensor and the verification of the relationship between its diagonal components for a thin plate should improve the understanding of this concept. In the context of distance learning, the problem of conducting an experiment on the aforementioned topic can be solved by studying torsional oscillations using easily accessible equipment.

Materials and methods. The study is based on the analysis of the physics course program for undergraduate students of a technical university, a review of the literature on the subject of the study. In the context of distance learning, the parameters of torsional oscillations of a rigid body can be determined using a monophyletic suspension and a smartphone with an MMS gyroscope, where running the PhyPhox or Physics Toolbox Suite application. The suspension can be made of a thin steel or copper wire, a rubber thread, or other suitable materials.

Results. The experimental determination of the periods of torsional oscillation of a smartphone relative to different axes showed that, regardless of the material of the elastic thread, the ratio  is fulfilled with an error not exceeding 6 %. This result confirms the relation between the diagonal components of the thin plate moment of inertia tensor
.

Conclusions. The study of torsional oscillations during a home experiment using simple equipment allows us to verify with sufficient accuracy the fulfillment of the relationship between the components of the tensor of the moment of inertia of a thin plate, the role of which is played by a smartphone equipped with an MMS gyroscope. The method used to suspend the smartphone on an elastic thread also allows us to determine the moments of inertia about axes that do not coincide with the axes of symmetry and to form a correct understanding of the angular velocity vector.