This note derives the well known Coriolis velocity (10) of the plane polar coordinate system as the generally covariant Cartan derivative (1) of ECE2 unified field theory. The Coriolis velocity includes the well known orbital velocity v = omega r of a circular orbit. Note carefully that this result is no longer true in an elliptical orbit. As shown in Note 362(2a), and computer algebra by co author Horst Eckardt, the elliptical polar system is needed for self consistency. The elliptical polar coordinates system is expected to produce new fundamental velocities and accelerations of classical dynamics, this is pencilled in for UFT363. A remarkable result of computer algebra is that Eq. (12) is also true in the elliptical polar system. The general vector field V(t, r, theta) in plane polar coordinates is given by Eq. (17), and its time derivative is the Lagrange derivative, Eq. (18). The spin connection from Eq. (18) will be given in the next note. In classical dynamics, V = V(t). Therefore if an orbit is observed to deviate from the result given by V = V(t), then it is logical to assume that the orbit must be analyzed by V = V(t, r, theta) within the overall structure of ECE2 generally covariant unified field theory, in which fluid dynamics, dynamics, gravitation and electrodynamics are unified by Cartan geometry. It is probable that this unification already encompasses the weak and strong nuclear forces, but this needs to be proven rigorously. UFT225 showed that conventional electroweak theory is a fiasco from which no conclusions can be drawn.