When a point P has polar coordinates (r,θ‎), the vectors e_r and e_θ‎ are defined by

where i and j are unit vectors in the directions of the positive x- and y-axes. Then e_r is a unit vector along OP in the direction of increasing r, and e_θ‎ 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 e_r and e_θ‎. Thus v = v₁e_r + v₂e_θ‎, where v₁ = v·e_r and v₂ = v·e_θ‎. 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)e_r(t), the velocity r′(t) has components r’ and rθ‎’ and acceleration r″(t) has components r’’ − r(θ‎’)² and r⁻¹(r²θ‎’)’.