In lecture 2 of his series on Classical Physics, Prof. Balakrishnan asks how many degrees of freedom there are in a system consisting of a falling piece of chalk. Looking at my notes, I'm not sure I understand the concept. Is the answer 6 (3 of position, 3 of orientation), or 12 (3 of position, three of orientation, 3 of linear velocity, 3 of angular velocity), or something else? Is the number of degrees of freedom the dimension of the configuration space, or of the phase space? Is there always a natural distinction between configuration space and phase space in dynamical systems?