For a path of radius r, when an angle θ is swept out, the distance traveled on the periphery of the orbit is s = rθ. Therefore, the speed of travel around the orbit is v = r d θ θ d t = r ω ω , where the angular rate of rotation is ω. (By rearrangement, ω = v / r.) Thus, v is a constant, and the velocity vector v also rotates with constant magnitude v, at the same angular rate ω.