Now let there be an object off of the rotating disk and at inertial rest with respect to the center of the disk and at a distance of R from it. This object has a coordinate motion described by dθ = − ω dt, which describes the inertially at-rest object of counter-rotating in the view of the rotating observer. Now the proper time equation becomes d τ τ = [ 1 − − ( R ω ω c ) 2 ] d t 2 − − ( R ω ω c ) 2 d t 2 + 2 ( R ω ω c ) 2 d t 2 = d t .