So for an observer rotating at a constant distance of r from a given point in spacetime at a constant angular rate of ω between coordinate times T 1 and T 2 , the proper time experienced will be ∫ ∫ T 1 T 2 d τ τ = ( T 2 − − T 1 ) 1 − − ( r ω ω c ) 2 = Δ Δ T 1 − − v 2 / c 2 , as v = rω for a rotating observer. This result is the same as for the linear motion example, and shows the general application of the integral form of the proper time formula.