Pulling a Spool

Abstract

A simple model for the kinetic frictional force on an object sliding across a surface is adopted in introductory physics. Its magnitude is given by a constant coefficient of kinetic friction multiplied by the normal force exerted on the object by the surface, and the force points opposite the direction that the object slides relative to the surface. In contrast, the standard model for the static frictional force is more complicated. There is no formula for its magnitude, but instead it can vary from zero up to some maximum value, as required to keep the point of contact of the object at rest relative to the surface it is on. Furthermore, it points in the direction opposite the way in which the object would slip at its point of contact if there were zero friction, but it is not always obvious which way that is. In an attempt to bypass these complications, students can make erroneous assumptions about the magnitude and direction of the static frictional force. To counter them, it is helpful to present some example that shows students that those assumptions need not hold. Such a system is a pulled spool that rolls without slipping on a horizontal table. Since the point of contact between the spool and the table does not slip, any frictional force between them must be static.