The classical approximated formula describing frictional force is [itex]f = N\mu[/itex], directed oppositely to the motion direction. What about that kind of friction that arises when N is 0? How can I account of that? For example, suppose I let a cylinder fall inside a pipe nearly the same size, so that air cannot slip through the cylinder and the pipe. The motion is perfectly vertical (parallel to gravitational force). The cylinder falls slowly than it would otherwise, and produces heat on the surface of the pipe, displaying evident friction. Still, no vector N exists since the cylinder is falling and does not stand on a surface.