We investigate the rotation sets of open billiards in  for the natural observable related to a starting point of a given billiard trajectory. We prove that the general rotation set is convex and the set of all convex combinations of rotation vectors of periodic trajectory  is dense in it. We provide a constructive proof which illustrates that the set  is dense in the pointwise rotation set, and the closure of the pointwise rotation set is convex. We also consider a class of billiards consisting of three obstacles and construct a sequence in the symbol space such that its rotation vector is not defined.

rotation theory, rotation vectors, open billiards, periodic trajectories, general rotation set.