  We consider a mechanical system consisting of an infinite rod (a straight
line) and a ball (a massless point) on the plane. The rod rotates uniformly
around one of its points. The ball is reflected elastically when colliding with
the rod and moves freely between consecutive hits. A sliding motion along the
rod is also allowed. We prove the existence and uniqueness of the motion with a
given position and velocity at a certain time instant. We prove that only 5
kinds of motion are possible: a billiard motion; a sliding motion; a billiard
motion followed by sliding; a sliding motion followed by a billiard one; and a
constant motion when the ball is at the center of rotation. The asymptotic
behaviors of time intervals between consecutive hits and of distances between
the points of hits on the rod are determined.
