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Centripetal force is the added tension force the rope exerts by "pulling" inward to keep an object moving in its arc and not in a straight line. An object being rotated around a central point via a rope (like a pendulum) exerts strain on the rope caused by centripetal force.
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The tension in a given strand of string or rope is a result of the forces pulling on the rope from either end. Define the forces on either end of the strand.