Galileoʼs kinematical paradox and the role of resistive forces

Abstract

We discuss Galileoʼs kinematical 'paradox' taking into account the effects of sliding friction and of resistive forces proportional to velocity. We show that sliding friction eliminates the paradox but still allows for very simple synchronous curves. Perhaps surprisingly, Galileoʼs paradox is preserved when the resistive force is proportional to velocity.