Introducing gyroscopes quantitatively without putting students into a spin

Abstract

The uniform precession of a simple form of gyroscope is analysed via a direct application of Newton's laws, using only concepts generally taught to physics and engineering students in the first two years of an undergraduate programme, with an emphasis on understanding the forces and torques acting on the system. This type of approach, in the middle ground between qualitative descriptions and detailed mathematical analysis of gyroscopic motion, provides a suitable vehicle to enable motivated students to bridge this gap later. The particular system analysed here, though basic, enables many important concepts and techniques of mechanics to be highlighted and utilized. The analysis enables students to arrive at a quantitative understanding of fast and slow gyroscopic precession and thus goes beyond previous treatments in this middle ground of qualitative/quantitative analysis and appears to be the reasonable upper limit of the capability of such analyses. The simple system analysed is also quite amenable to construction and demonstration as part of a wider project-based approach.