Physics in Non-inertial Systems

Abstract

Despite appearances, Newton’s dynamics is not simple at all, nor very intuitive. The three fundamental principles, for example, took centuries before they were recognised as true, as our collective experience tells us that bodies don’t move unless a force is applied to them. Galileo Galilei first realised that friction is responsible for this, a fact that is not straightforward in the absence of Newton’s first Law. Many conceptual difficulties in classical mechanics, such as those connected to Newton’s third Law or to the usage of non-inertial reference frames, can be at least partly ascribed to the confusion between the term force and the term interaction. Forces are the result of interactions, and interactions are only effective among at least two entities. In this respect, what we call fictitious or apparent forces can be considered, in fact, to be as real as gravity or the elastic force. On the other hand, we can measure them, thus they exist. The confusion comes from the fact that, in the past, forces and interactions were, in fact, used as if they were synonyms, as any interaction gave rise to a force, represented as a vector in Newtonian mechanics. Today, we know that this is not always the case. The weak interaction, for example, is responsible for radioactive decays. The interaction causes the change of state of a system composed of an atom of a given species into another in which the state is composed of an atom of a different species, together with one or more particles (a photon, an \(\alpha \)-particle or an electron and a neutrino). There is no place to which we can attach a vector in this case, hence there is no force, in the Newtonian sense. It would be better for us to say that interactions are responsible for the change of state of a system and the effects of interactions often can be, but are not always, represented by forces. In this chapter, we perform experiments in which we explore the physics in non-inertial frames, to dissipate doubts and to allow you to familiarise with them. This chapter introduces topics that are often only marginally covered in physics books. We perform experiments in a rotating reference frame and, interestingly enough, in a free-falling system. It is an interesting experiment, that today we can perform, thanks to the availability of tools like smartphones, but, in the past, it was considered an experiment that could only be conducted mentally: a gedankenexperiment. We learn the principles of operation of gyroscopes and study the Euler acceleration in a rotating bucket.