Hold one end of a long string of beads and get it twirling around a vertical axis with a vigorous stirring motion (like in some cowboy lasso tricks, but without the noose loop). As the speed increases the middle of the string pulls outward, drawing the lower end up, until the bottom part looks horizontal. Since the top is basically fixed it makes a cusp, and overall the profile the whole string traces in the air is shaped something like an onion, oriented cusp-up, like the Mogul-style onion domes seen on many buildings. At high speeds the string gets sharply bent, like a hairpin. Can you give an expression describing the "onion curve" the string forms at a given speed? What path does the string's bottom end trace as a function of the speed of rotation?