Abstract: In this paper，the general calculation formula of curvature radius of two-dimensional curve in polar

coordinate system is derived respectively by using the rectangular coordinate calculation formula and mechanical

vector calculation formula of curvature radius of two-dimensional curve. Then the formula is used to get the uniform

expression of the curvature radius of the conic in the usual polar coordinate system，according which the expressions

of the curvature radius of each conic in the usual rectangular coordinate system are derived. This paper also uses the

relevant dynamic conclusions of planetary orbit motion to directly deduce the unified expression of curvature radius

of conic curve in the usual polar coordinate system，and points out the equivalence of mathematical and mechanical

reasoning methods，as well as the reason why the latter is often more simple.

Key words: polar coordinate system, curve, curvature radius, calculating formula, mechanics