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You will fly out in a straight line tangent to the circumference of the merry-go-around at the precise point you lost grip (inertia) and down (gravity) in the same direction of the rotation of the merry go round On the merry-go-round your inertia is trying to send you in a straight line, and the merry-go-round is pulling you inward and deflecting your motion so that you go in a circle. If you are holding on to a pole with your hands, you'll feel the tension as it pulls on you. (In accordance with Newton's third law of motion, you pull back on the pole just as hard as it pulls on you.) The merry-go-round's force makes you accelerate inward and you feel all the mass in your body resisting this acceleration. As the force is conveyed to your body through your muscles, you feel your body resisting the inward acceleration. There's no real outward force on you; it's just your inertia fighting the inward acceleration. When you ride on the outer edge of a merry-go-round, there is only one force on you and that force is inward (toward the center of the ride). That force is called a centripetal force, meaning toward the center. As for your tendency to travel in a straight line, that's just the your inertia. With no forces acting on you, you will obey Newton's first law and travel in a straight line. There is no real force pulling you outward. But you will feel pulled outward. That is called a fictitious force. Fictitious forces always appear in the direction opposite acceleration. In this case you, the outward fictitious force is called "centrifugal force." But remember that it's not a real force; it's just your inertia trying to make you go in a straight line. Finally, when you let go, the resistance (fictitious force) is lost and your inertia carries you out in a straight line from the point where you lost grip and tangent to the circumference of the merry-go-round. Gravity will pull you down to the ground.

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