To evaluate the velocity, the derivative of the unit vector u ρ is needed. Because u ρ is a unit vector, its magnitude is fixed, and it can change only in direction, that is, its change d u ρ has a component only perpendicular to u ρ. When the trajectory r (t) rotates an amount d θ, u ρ, which points in the same direction as r (t), also rotates by d θ. See image above. Therefore, the change in u ρ is