Circular motion concepts

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1. The problem statement, all variables and given/known data
how come that if I grab a stone and attach it to a string and then rotate it along the xy axis it wont fall even though there is acceleration from gravity in the z axis where no force is applied?


2. Relevant equations



3. The attempt at a solution
maybe its the fact that I am holding the string comes to play I don't know.
 
Notice that if you perform such an experiment, you'll need to swing the string at an angle constantly. If your own hand is in a x-y motion, yes the stone would drop. But if you want to swing the stone above your hand, what you're actually doing is swinging with a x-y-z component force.

If you draw a free-body diagram, there should be mg acting on the stone, tension of string, T, and the swinging force provided by the hand that is in the opposite direction of the tension. After all forces resolve, there should be the centripetal force only.
 
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The stone isn't in the same xy plane as the point where you're holding it. It's somewhat lower, displaced along the z axis. The harder you swing the stone, the less that displacement will be, but it will never be zero. There will always be a component which, when multiplied against the centripetal force generated by the orbiting stone, will be enough to counteract the force of gravity on the stone.
 

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