Starting with a discussion of what I call ‘Koyré's paradox of conceptual novelty’, I introduce the ideas of Damerow et al. on the establishment of classical mechanics in Galileo's work. I then argue that although their view on the nature of Galileo's conceptual innovation is convincing, it misses an essential element: Galileo's use of the experiments described in the first day of the Two New Sciences. I describe these experiments and analyze their function. Central to my analysis is the idea that Galileo's pendulum experiments serve to secure the reference of his theoretical models in actually occurring cases of free fall. In this way, Galileo's experiments constitute an essential part of the meaning of the new concepts of classical mechanics.