Let there be an observer C on a disk rotating in the xy plane at a coordinate angular rate of ω ω and who is at a distance of r from the center of the disk with the center of the disk at x = y = z = 0. The path of observer C is given by ( T , r cos ⁡ ⁡ ( ω ω T ) , r sin ⁡ ⁡ ( ω ω T ) , 0 ) , where T is the current coordinate time. When r and ω ω are constant, d x = − − r ω ω sin ⁡ ⁡ ( ω ω T ) d T and d y = r ω ω cos ⁡ ⁡ ( ω ω T ) d T . The incremental proper time formula then becomes d τ τ = d T 2 − − ( r ω ω c ) 2 sin 2 ⁡ ⁡ ( ω ω T ) d T 2 − − ( r ω ω c ) 2 cos 2 ⁡ ⁡ ( ω ω T ) d T 2 = d T 1 − − ( r ω ω c ) 2 .