It is my understanding (and ive just started studying this stuff so its very probable I've got the wrong end of the stick) that if you whirl a heavy object in a consistant orbit that the velocity and its mass (force) of the object being whirled around is always tangential to the point that the object is on the circle. Like if the string was cut - the ball would fly off at 90 degrees to the line of the centrifugal pull out.....
Not going to get into the TGM part of it, because I don't have the book here to reference, but from a physics view point...
Be careful with the words you use. Mass is not a force, never will be. An object when travelling in a circle will have instantaneous velocity at a tangent to the circle, and instantaneous force (and therefore acceleration) towards the centre of the circle, in your case this force is tension in the string.
When one cuts the string, that force towards the centre of the circle gets removed, therefore there is no force (and therefore no acceleration) on the rock, so you are correct, it will fly off tangential to the circle.
Will expand on TGM side of it once I have the book in front of me (don't have the diagrams memorised yet..sorry)!!
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