One can differentiate to find velocity: v = r d u r d t = r d d t ( cos ⁡ ⁡ θ θ i ^ ^ + sin ⁡ ⁡ θ θ j ^ ^ ) = r d θ θ d t d d θ θ ( cos ⁡ ⁡ θ θ i ^ ^ + sin ⁡ ⁡ θ θ j ^ ^ ) = r d θ θ d t ( − − sin ⁡ ⁡ θ θ i ^ ^ + cos ⁡ ⁡ θ θ j ^ ^ ) = r d θ θ d t u θ θ = ω ω r u θ θ where ω is the angular velocity dθ / dt.