Five ways of deriving the equation of motion for rolling bodies

摘要

The equation of motion for rolling bodies can be derived in several different ways. This paper shows that the equation of motion can be derived in five and only five ways without needing to know the normal and frictional forces acting at the point of contact. After enumerating these five ways, we examine two illustrative examples: an asymmetric disk rolling on a cylinder and a symmetric ball rolling on a turntable. We also discuss the educational benefits of including this topic when teaching mechanics.