In a similar fashion, the rate of change of u θ is found. As with u ρ, u θ is a unit vector and can only rotate without changing size. To remain orthogonal to u ρ while the trajectory r (t) rotates an amount d θ, u θ, which is orthogonal to r (t), also rotates by d θ. See image above. Therefore, the change d u θ is orthogonal to u θ and proportional to d θ (see image above):