The basic working principle of a high-speed centrifuge involves placing a sample in a rotor that spins at high speeds. The centrifugal force generated is proportional to the speed of rotation and the radius of the rotor. This force acts on the particles in the sample, causing them to separate based on their density. Heavier particles move outward while lighter ones stay closer to the center. This separation is particularly useful in catalysis, where the physical state of catalysts and products can vary greatly.