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What happens in the absence of the centripetal force?

As you whirl the rock around your head by a string, you exert a force on the string and the string exerts a force on the rock toward the center of the circle. Then, the rock accelerates toward the center of the circle causing it to move in a circle at a constant speed. Consider what would happen if you cut the string in the middle of the swing. Look at the picture—at top view of the rock going in a circle—and think about which direction the rock would fly.

a rock moves with circular motion and the string is cut, what direction would the rock fly: A- straight out from the center, B- at an angle away from the center, C- tangent to the circle

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When the rock is released, the centripetal force is removed, and the rock no longer moves in a circular path. At the moment the rock string is cut, the velocity of the rock points tangent to the circle, thus its inertia causes the rock to move in a path tangent to the circular path. The answer is path C.