Fouettes and Physics

My friend is in the Fuse Dance Company here at Colgate, and after watching a clip of her group dancing, I could not help but to think about the physics concepts we learned in action. I was technique to master. Fouetté is a classical ballet term that refers to the "quick, whipping movement of the raised leg in ballet, usually accompanying a pirouette" (Merriam-Webster). This idea immediately reminded me of rotational motion. I noticed that the dancer could control the speed of her turns based on the extension or retraction of her free leg (i.e, the leg that is not spinning). This can be understood in terms of moment of inertia. We know from the moment of inertia formula for a point mass, that I α radius (which is the perpendicular distance from the axis of rotation). If we look at the dancer’s spinning body as her axis of rotation and arms/legs as point masses, we could see that the movement of her arms and free leg causes changes in her moment of inertia. This is because the distance between her mass and axis of rotation vary during the sequence. To relate this to speed, we know from the rotational KE formula that I and angular velocity are inversely proportional. As her mass is distanced from her axis of rotation, her moment of inertia increases, thereby decreasing her angular velocity. Therefore, when the dancer extends her leg, she creates a larger moment of inertia and slows down. When she retracts her leg, she decreases her moment of inertia and increases her angular velocity, causing her to turn more quickly.