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If a rope is wrapped aound a cylinder what is the relationship between the amount of wrap and the ability to resist slipping off of the cylinder? An example would be if I had a 180 degree wrap and attached a 100 pound weight on one end of the rope, what force would be required to hold the other end? What if the rope wrapped 360 degrees around the cylinder and so on?

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It's known as the capstan equation

The force the rope can hold is exponential with the total wrap angle (or number of turns)

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