The centripetal acceleration is the radial component, which is directed radially inward: a R ( t ) = − − ω ω 2 R u ^ ^ R ( t ) , while the tangential component changes the magnitude of the velocity: a θ θ ( t ) = R d ω ω d t u ^ ^ θ θ ( t ) = d R ω ω d t u ^ ^ θ θ ( t ) = d | v ( t ) | d t u ^ ^ θ θ ( t ) .