Usually centripetal/centrifugal forces are illustrated showing a cord with a small mass attached as shown in Fig1a.  However equally interesting is to show these forces with a hollow cylinder.  In one case a pulling force toward the center of rotation in the other case a pushing force again toward the center of rotation. Centrifuges are used in a variety of cases. For example a dryer where centrifugal force is what dries the clothes. Huge centrifuges are used to expose astronauts to extreme forces. The outward force created by such a large machine can be used to simulate the massive G-forces that an astronaut or fighter pilot is likely to experience. Scientists use the centrifuge to test these forces on people in a controlled environment.  Centrifuges are used in wastewater management, in the oil industry, and even in the processing of sugar and milk. They are also used in the nuclear power industry to separate isotopes and enrich uranium.  (wisegeek.com).  There are many devices engineers happily refer to as, centrifugal governor, centrifugal pump, centrifugal compressor, centrifugal dryer - not bad for a force which does not exist.

Above various free body diagrams of the spring mass system. Gravity is ignored. In Fig2a The mass and the spring are considered as one unit; the only external forces acting on it are a centripetal force and an applied torque. In Fig2b the spring is considered separately - the forces acting on it are, on the left side, the centripetal and the applied torque. On the right side the centrifugal force and a transverse force exerted by the mass on the spring.  In Fig2c we have isolated the mass. On it are acting the centripetal force and a transverse force exerted by the spring on the mass. In Fig2d the forces are shown  acting on the inner pivot - a reaction torque and the centrifugal force.

Fig3 a/b show the mass spring system and the torque applied  for a certain time at the center. Figs 4 a/b/c/d show the force vectors acting on the mass. First only the centripetal force, than coriolis force added, and subsequently transverse and radial inertial force.

mandrin