Page "Centripetal force" Paragraph 94

where the notation ρ is used to describe the distance of the path from the origin instead of R to emphasize that this distance is not fixed, but varies with time.

The unit vector u < sub > ρ </ sub > travels with the particle and always points in the same direction as r ( t ).

Unit vector u < sub > θ </ sub > also travels with the particle and stays orthogonal to u < sub > ρ </ sub >.

Thus, u < sub > ρ </ sub > and u < sub > θ </ sub > form a local Cartesian coordinate system attached to the particle, and tied to the path traveled by the particle.

By moving the unit vectors so their tails coincide, as seen in the circle at the left of the image above, it is seen that u < sub > ρ </ sub > and u < sub > θ </ sub > form a right-angled pair with tips on the unit circle that trace back and forth on the perimeter of this circle with the same angle θ ( t ) as r ( t ).