The'Typical particle' approach to learning rigid body dynamics

Rigid body dynamics is a foundational course in all engineering curricula based upon the mechanical sciences. It is one of three courses that make up The Mechanics Project, an effort at a large R1 university in the southwest, to reimagine the learning experience in the sophomore-level engineering mechanics courses (statics, dynamics, and deformable solids). The conversion of these courses to an objective-based system to assess mastery launched a reconsideration of the fundamental strands-the DNA-of the courses. The design objective of focusing learning as much on 'why' as on 'how' suggested that students should learn how to derive equations of motion from first principles. This approach led to a set of objectives that are a framework to solve any rigid body dynamics problem. The resulting approach differs from the more traditional approach with special equations, already derived, to solve certain types of problems (which can promote plug-and-chug problem solving). Our approach is built around the description of the position vector of a typical particle in the system. From there, students sum forces and moments over all the particles to get the equations of motion, essentially leading them through the steps that Euler took to generalize Newton's laws of motion. Each problem requires the student to visualize and mathematically describe the motion of the system at hand. This approach allows the students to see where the equations of motion come from, it provides a unique opportunity to master vector notation, and it reinforces and improves skills in calculus and differential equations. This paper describes our approach to learning dynamics with an example to show the key role of the position vector in the setup of every dynamics problem.