Let's try another merry-go-round example.
Suppose you are located on the edge of a merry-go-round and with the left hand you hold on to the metal bar handle thing, and with the right hand you hold a 20lb dumbbell. Now suppose someone else spins up the merry-go-round for all that it's worth.
Once in motion, your left arm is applying the centripetal force necessary to keep you on the merry-go-round. Your right arm is supplying the centripetal force necessary to keep the 20lb dumbbell in your hand. Pretty soon however things start to change as the muscles in your right hand and forearm (which are supplying the grip on the dumbbell and hince the centripetal force that keeps the dumbbell moving in an arc) start to get tired.
But wait, there's another complication. Since you started this strange experiment, a rather large crowd has gathered around the merry-go-round to look at this unusual sight. You soon realize that if you relax your tired grip on the dumbbell, somebody is going to get seriously hurt. You call out to your companion to slow down the merry-go-round, but for some strange reason (the noise of the crowd?) he can't hear you.
Now you have a real delimma on your hands, and this situation (like all serious situations) starts to focus and clear your mind. While your muscles are getting weaker and weaker and the dumbbell is trying to pull your arm out of its socket, you have to decide if centrifugal force is really an actual force or not. You know your arm is really starting to feel the "pull" of the dumbbell and the pain is starting to become extreme. You also know that if you let go, somebody is going to get a stomach full of fast moving dumbbell, which you know will hurt a great deal.
Quickly you decide that centrifugal force, which acts against centripetal force to try and cause an object to travel in a straight line, is real enough. Therefore as a skilled pilot trained to think quickly and to act in an emergency, you hastily decide to yell out to the gathered crowd to quickly move away from the merry-go-round. As soon as they do, you release the grip on the dumbbell (to the great relief of your arm) and watch as centrifugal force instantly transforms the circular course of the dumbbell into a linear course of free flight through the air. Then you watch as the centripetal force of gravity pulls the dumbbell towards the earth's center of rotation, and causes it to crash into the ground a good number of feet in front of you.
Thus this wonderful experiment demonstrates that centrifugal force is in fact a real force.
(edited for spelling errors and typos)
[ 17 December 2001: Message edited by: Flight Safety ]