A general rotating frame formulation of the Navier-Stokes equations has been added to the incompressible and arbitrary Mach number versions of UNCLE. While eliminating the need for moving grids, this formulation also reduces the error caused by linear approximations of rotational motion. The formulation is validated for single axis rotations by comparing the simulations of a marine propeller and an isolated helicopter rotor with experimental data. A simulation of the helicopter rotor in pitching motion is also performed. Results are compared between the non-inertial reference frame formulation and absolute frame solver for a prolate spheroid with all the components of angular velocity. The use of the non-inertial reference frame promises a faster and more accurate six-degree-ofreedom simulations.