Asymmetric rolling bodies and the phantom torque

The center of mass and the point of contact of two-dimensional rolling bodies are used almost interchangeably to understand the dynamics of rolling bodies in introductory physics courses. The use of the contact point has the virtue that one does not need to know the normal and frictional forces at the point of contact. However, the correct use of the point of contact requires a concomitant torque that we call a “phantom torque.” This torque vanishes for azimuthally symmetric bodies that are conventionally used as examples in introductory physics courses and, thus, goes unnoticed. We show that the phantom torque can be evaluated easily.