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I know this is a basic question, but question:

A rock is connected to one end of string and is in circular motion with the center being the other end of the string. Now the string gets released at some point. How do we know the direction in which the rock is going to fly?

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What do you know about the forces on the rock? What do Newton's laws tell you about the subsequent motion of the rock? –  Jerry Schirmer Sep 3 '13 at 3:54
    
What about a catapult? Does anything make the rock/string system different from that? –  Robert Mastragostino Sep 3 '13 at 4:00
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1 Answer

Let our frame of reference be the center of this circle. After the string is released, in this frame, there is no net force on the rock (we are pretending our system is isolated, i.e., we are ignoring things like gravity that we would obviously have to take into account in the 'real world'). Under the assumption that our frame of reference is inertial, this implies that the acceleration of the rock is $0$, i.e., has constant velocity. To figure out what this constant velocity is, just look at whatever the velocity was just before the string was released. It was moving tangent to the circle before (this motion was forced on it by the tension in the string), and hence it will 'fly out' on a line tangent to the original circle.

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This explanation would be more fitting to a real life situation, if you consider the acceleration of the rock as $g$ after the string is cut. In that case the rock will follow projectile motion. –  udiboy Sep 3 '13 at 15:44
    
Even if you consider the gravity the the stone which is released will exhibit a horizontal projectile motion where the horizontal velocity is constant and the vertical velocity is similar to the case of dropping the stone from a height –  shivaraj Sep 3 '13 at 16:11
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