h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Forces always come in pairs. An unbalanced or unpaired force will always result in something moving. In the case of a yo-you being spun about by means of holding a string, for instance, as long as you are holding onto the string, the tension on the sting produced by the yo-yo must be counterbalanced by you maintaining a force keeping the string at or near the center of rotation.

Since the yo-yo does not move closer or further away, the paired force in this case would be a 'centripetal' (towards the center) force provided by you, balanced against a 'centrifugal' (away from the center) force, that inexplicably is in a direction other than tangential. Drawing the force as though it were tangential does not resolve the force diagram either. If released, the yo-yo cannot resolve to a resultant motion that is closer to the center than the tangential, can it?

But since we know that the vector sum of these forces cannot predict the tangential path of the yo-yo when the string is released, ONE of them must be somehow 'fictitious'. It is somewhat arbitrary that the choice for the fictitious force / acceleration in this case is the one we call 'centrifugal'.

'Fictitious' is perhaps a bad name for it, but I hope this clears it up. It is rare for a physics teacher to know enough about the resolution of vector force diagram to point out the reason for this term as it applies to circular motion of a particle on a string.