Why doesn't Centrifugal Force cancel out Centripetal Force acting on a stone in circular motion?

Suppose a stone is set in circular motion using a string, why doesn't the centripetal(radial force) not negate the Centrifugal force acting upon the same stone, although they are equal in magnitude and opposite in direction? Technically, as the two forces are equal in magnitude and opposite in the direction, they should negate each other, and the stone should attain a state of rest, right?Why doesn't Centrifugal Force cancel out Centripetal Force acting on a stone in circular motion?That's an excellent point. The explanation is that there ISN'T ANY "ceftrifugal force" acting on the stone.



The frame of reference that most physics books choose is an inertial frame in which the stone is seen to move in a circle. In that frame, there's only one force--it's centripetal, and it's due to the tension of the string. This force causes the stone's direction of motion to continually change, in accordance with Newton's laws. There isn't any force pulling OUTWARD on the stone.



There IS, however, a force pulling outward on the STRING. This agrees with Newton's 3rd Law; which says that as the string pulls inward on the stone, then the stone must pull outward on the string. This is sometimes confused as meaning that something is pulling outward on the stone as well; but that's not the case.



An alternate way to look at it is from a reference frame that that is moving along with the stone (e.g., pretend you have a little laboratory set up on the stone, and you make your measurements from there.) In THAT reference frame, there ARE two forces acting on the stone; one "centripetal" (due to the string's tension); and an opposing "centrifugal" force. However, in THAT reference frame, the stone IS "at rest," so there is no contradiction.