This result for the velocity matches expectations that the velocity should be directed tangentially to the circle, and that the magnitude of the velocity should be rω. Differentiating again, and noting that d u θ θ d t = − − d θ θ d t u r = − − ω ω u r , we find that the acceleration, a is: a = r ( d ω ω d t u θ θ − − ω ω 2 u r ) .