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As the rock moves along its curved path, the applied force suddenly goes to ZERO at point P.  This means the net force becomes zero.  From Newton’s 1st law, we know that when the net force is zero the object moves in a straight line at constant speed.  In this situation, along what straight line will the rock travel?

The answer can be found again from Newton’s First Law.  When the force goes to zero, the object will travel along a straight line in the direction it was traveling WHEN the force went to zero.  If you remember the demo from class, you will remember that the rock will now travel along the tangent to the circle.

If the force goes to zero at point P, the rock will travel in a straight line along the direction of the tangent to the circle at P.

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