OK, here goes...
You are both (Lu and Nick) partly right and partly wrong. I've never taught Newtonian physics, but I'm otherwise quite good at it. For review lets look at Newton's 3 laws of motion, which are needed in order to shed the light necessary to understand both the centrifugal and centripetal forces (both of which are real).
Newton's first law of motion, expressed in 3 different ways...
A Every object in a state of uniform motion tends to remain in that state of motion, unless an external force is applied to it.
B An object in motion tends to stay in motion, and an object at rest tends to stay at rest, unless the object is acted upon by an outside force.
C An object in a state of motion possesses an "inertia" that causes it to remain in that state of motion unless an external force acts on it.
Galileo formulated the basic concept of "inertia", which served as the cornerstone for Newton's first law of motion.
Newton's second law of motion, expressed in 3 different ways...
A The relationship between an object's mass m, its acceleration a, and the applied force F, is a = F/m or F = ma. Acceleration and force are vectors. In this law the direction of the force vector is the same as the direction of the acceleration vector.
B Acceleration = Force/Mass. This is usually shortened to A=F/M or F=MA. Since acceleration is the rate at which speed changes, it is usually expressed in units of m/s/s (every second, the object which is accelerating will go that much faster). Force is usually expressed in Newtons (N), wich are kgm/s/s (you can see why they changed the name to newtons!)
C Newton's Second Law is more abstract than the First. The Second Law governs all acceleration and is really very simple -- acceleration is produced when a force acts on a mass. The greater the mass (of the object being accelerated) the greater the amount of force needed (to accelerate the object).
Newton's third laws of motion, expressed in 2 different ways...
A For every action there is an equal and opposite reaction.
B Every action has an equal and opposite reaction. These actions are forces, so you can remember this law as being every force has an equal and opposite force. Remember that these are two separate forces which act upon two separate objects, and so they do not cancel each other out, and the magnitude of these forces is equal.
There are a few side effects of these laws that are worth covering. Newton's first law implies that any object once set in motion, will stay in motion, continuing at the same speed in the same direction, until an outside force acts on it. This is often called a motion "vector". "Momentum" is a more sophisticated definition of "inertia" that includes values of mass, speed, and direction.
Newton's second law (acceleration equals force divided by mass) is satisfied when vector arithmetic is used to solve the problem of applying multiple acceleration forces to an object at the same time. Vector arithmetic resolves the multiple forces (including the object's original "momentum vector") down to a single (summed) vector, which then shows how the object's motion will change when all the forces are applied. While this is too complicated to get into here, the result will be a simple (and observed) change in the acceleration and direction of the object. It's when there are several forces acting in 3 dimensions (and when the forces are being applied at different times) that this starts to get really complicated.
With this review out of the way, let's cover the subject of centrifugal and centripetal forces.
We often think of a rotating object as having "angular momentum". This momentum consists of both speed and mass, but direction is a problem since the object is rotating. "Coning" rotor blades show that this "inertia" or momentum is preserved by speeding up the rotation or slowing it down as the rotor blades "cone" up and flatten out again.
But all objects in motion obey Newton's first law, since once they are set in motion, they continue in a straight line until acted on by an outside force. Centrifugal force is nothing more than Newton's first law being expressed by the moving object, namely "inertia" or momentum desiring to travel in a straight line.
It's interesting however that centrifugal force does not exist unless centripetal force is also being applied. As stated elsewhere, centripetal force draws an object to a center of rotation. Once a centripetal force begins to act on a moving object, centrifugal force acts to try and keep that object traveling in a straight line, and the 2 forces oppose each other. When a centripetal force is relieved (such as when a rotor blade fractures) the part of the blade no longer attached to the rotor will travel in a straight line away from the center of rotation (the hub). This will occur because the "inertia" or momentum of the rotating blade that was previously expressing itself as centrifugal force, will now express itself by causing the blade to travel away from the hub in a straight line (setting aside aerodynamic factors), as the blade's momentum resists changes in its direction.
To put it another way, "inertia" or momentum can express itself in a variety of ways. Aerodynamic drag is a form of "inertia" in that previously stationary (relatively speaking) air molecules are being forced to move out of the way by a passing aircraft. It's the "inertia" of running water (and its tendency to travel in a straight line) that carves out river canyons and turns old fashioned water wheels. So centrifugal force is "inertia" or momentum expressing itself against a centripetal force pulling a moving object toward a center of rotation.
I know this was long winded, but I hope it helps.
(edited for spelling errors and typos)
[ 16 December 2001: Message edited by: Flight Safety ]