Rules for rolling as a rotation about the instantaneous point of contact

It is a widespread misunderstanding in introductory physics courses that the motion of rolling bodies in general can be calculated using the point of contact as a reference point when equating the rate of change of angular momentum to the torque. In this paper I discuss in general two correct rules to be used instead, in order to derive the equation of motion of rolling bodies, taking moments about the point of contact. I also clarify that the point of contact either can be reckoned the fixed point on the rolling body instantly at the point of contact or the geometrical point defined as the point of contact at any time. Altogether this gives four different ways of deriving the equation of motion with some of them being easier than others depending on the case under consideration. The four different methods are as an illustration applied to a case presented recently by Turner and Turner (2010 Am. J. Phys. 78 905-7).