A method of pumping gaseous matter comprises a step of providing a pump rotor, intake port, exhaust port, and gas passageway. The gas passageway operatively connects the intake port to the exhaust port. The exhaust port is radially farther from the rotor's center axis than is the intake port. The method also includes a step of providing a stator and a step of rotationally driving the pump rotor relative to the stator in a manner causing gaseous matter to enter the gas passageway of the pump rotor via the intake port, to gain energy, and to move radially away from the center axis and out of the exhaust port. The gaseous matter has a supersonic velocity relative to the stator upon exiting the exhaust port. The method can be used to evacuate or compress gaseous matter.