Physics News Part I: Physics Behind Spins

 

Probably like many other girls, I was sent to ballet school since I was very little. From the practices in the studio and the performances on the stage, I learnt that nothing elicits cheers from an audience quite like a truly huge series of fouette en tournant, and the choreographer seem to add them here and there as a cheat to make people cheer. The turn normally constitute a whipping movement of the leg, during which the dancer turns on one foot while making fast outward and inward thrusts of the other leg at each revolution. I remember when I was first taught the move, I was instructed to prepare for the turn with my arm open, and close it in front of my chest during the turn. I did find the turn to be much smoother and less effort was needed to be exerted to complete each revolution. The other day, when my roommate, who also happen to be a future skater, was showing me one of her practice skating videos, I saw that during a spin she started off in a standing position and spins about the vertical axis, but after a few rotations, she pulled both arm in closer to the body and the spins were significantly faster. 

Having learnt the physics in rotational motion, now I can see why in both cases——a dancer performing turns on the floor and a figure skater performing a spins on ice——the rotational speed (i.e. angular velocity) about the vertical axis increases. This is because having the arms open means more mass are further away from the axis of, and the moment of inertia is larger than if that was was close to the axis. Because the moment of inertia is inversely related to the angular acceleration, the reduced moment of inertia when arms and a leg are drawn inward closer to the rotating axis gives a higher angular acceleration and a faster angular speed. Furthermore, if we were to go a step further and have a little fun with it, we could take some measurements of the angular velocity as revolutions per second both before and after the arms being pulled in. From that, we could then calculate the change in the moment of inertia----and therefore the mass of the arms that were pulled inward :-)