radial and transverse components
where i and j are unit vectors in the directions of the positive x- and y-axes. Then er is a unit vector along OP in the direction of increasing r, and eθ is a unit vector perpendicular to this in the direction of increasing θ. Any vector v can be written uniquely in terms of its components in the directions of er and eθ. Thus v = v1er + v2eθ, where v1 = v·er and v2 = v·eθ. The component v1 is the radial component, and the component v2 is the transverse component. For a particle with position vector r(t) = r(t)er(t), the velocity r′(t) has components r' and rθ' and acceleration r″(t) has components r'' − r(θ')2 and r −1(r2θ')'.