Shape of a Rotating Slinky

Abstract

If a Slinky suspended in a U-shape is rotated horizontally, it will have the shape of an upside-down [Formula: see text], like [Formula: see text], due to the centrifugal force in the horizontal direction acting on each point of the Slinky. In this paper, we discuss the shape of a rotating Slinky in both theoretical and experimental aspects. The rotating Slinky has the shape described by a multi-valued function if the angular velocity of the rotation satisfies [Formula: see text]. Our theoretical results are in good agreement with experimental observations. The video of the experiments can be viewed at https://youtu.be/rpu9Ol2jdAM .