Mounting a molecular beam source near the tip of a hollow high-speed rotor provides a means to shift the velocity distribution of the beam downward or upward over a wide range. We describe the construction of such a device and experiments and model calculations characterizing its operation, for both supersonic and effusive beams of rare gases, O-2, CH3F, and SF6. For example, the flow velocity of a rotating supersonic beam of O-2 was accelerated to above 1000 m/s (corresponding to a kinetic energy of 2200 K and deBroglie wavelength of 0.1 Angstrom) and decelerated (when seeded in Xe) to below 70 m/s (corresponding to a kinetic energy below 10 K and deBroglie wavelength of nearly 2 Angstrom). With improvements in prospect, the rotating beam source offers a versatile and relatively simple way to enhance techniques for manipulating molecular trajectories.