We discuss the angular velocity ([image omitted]) and angular acceleration ([image omitted]) associated with a particle in rectilinear motion with constant acceleration. The discussion was motivated by an observation that students and even teachers have difficulty in ascribing rotational motion concepts to a particle when the trajectory is a straight line. We present some details of our observations. A formal derivation of [omega] and [alpha] is presented which reveals "surprising" and non-intuitive aspects, namely non-monotonic behaviour with an associated extremum. The special case of constant velocity is studied and we find that angular acceleration associated with it also has an extremum. We discuss a plausible source of difficulty. (Contains 1 table and 3 figures.)