# How do figure skaters get angular momentum for a spin?

It’s no use asking skaters how they get the angular momentum for a spin. They don’t understand the distinction between angular momentum and velocity, and many are under the illusion that pulling in their arms is what gets them angular momentum.

Very shortly before the spin, there must be some sort of external torque upon the skater’s body (counter-clockwise torque for right-handed skaters). I am weighing various hypotheses:

1. The ice applies a reactive torque upon the weight-bearing pivot foot itself, but I cannot imagine how the skater would apply a clockwise torque to the ice with that foot. (Note that the resistance to turning is not very high, but it is not negligible either. During the spin itself, the skate does not pivot on a point. It leaves a tiny circular tracing on the ice.)

2. When shifting weight from the RBI edge to the LFO edge to enter a forward spin on the left foot, the skater pushes off in a particular direction with their right foot, and the ice pushes back. The resulting torque would depend on the direction of the push and the moment arm to the skater’s CM at the time. [Jargon defined: RBI = right backward inside; LFO = left forward outside.] (Note that the tracing left by the LFO entry edge has a counter-clockwise curvature even before the skater does a 3-turn and pulls in his/her arms.)

3. The pivot foot’s toe pick plays a role, digging into the ice and exerting a force. This could occur during the weight-shifting transition and before the CM is centered over the pivot foot. (Skaters say that they can’t do a spin without a toe pick, but the pick doesn’t leave much of a mark on the ice, so I don’t quite believe them.)

Please help me figure this out before I lose my faith in the conservation of angular momentum. It’s making me dizzy, and I just can’t chill out.

EDIT: I'm looking for insight into the directions of external forces (ice vs foot) and moment arms (CM vs foot) that act to create the torques.

• It's worth noting that you can't analyse the physics of combination (flip and twist) dives correctly without taking account of how the diver changes their whole inertial tensor, so you may be running into trouble from trying to use too simple a model of the body. See, for instance, C. Frohlich, Am. J. Phys. 47, 7. The result is that the question might be quite involved. (That reference can be found in the AAPT publication "Selected Reprints: Physics of Sports" which is fun to have on the shelf.) – dmckee Feb 2 '18 at 20:13
• The skater is skating a curve (so body at an angle then straightens), kicks a leg and arms out, then brings the leg and arms in to increase the rate of rotation. SEe video youtube.com/watch?v=Kk6pV0SzlMY at about 2:10 – MaxW Feb 2 '18 at 20:27
• – Farcher Feb 2 '18 at 20:46
• I won't answer as a physicist because as @dmckee says it's probably highly involved but I'll answer as a skater and say that a torque doesn't feel like a mystery at all to me: I positively can't begin a spin without the toe pick and have a definite, strong physical sensation of an off-center force. It's almost as though "spin" and "dig in toe" (metaphorically speaking, you don't actually need much dig at all) feel like the same command from my brain. I'm certainly not the most accomplished at this manoeuvre because it's certainly not my favorite thing to do: I can't spot well .... – WetSavannaAnimal Feb 2 '18 at 23:17
• ... and thus end up feeling really ill after any spin, particularly now I'm 54, but I really don't think there is any other way you can get the torque needed. On second thoughts, a sideways skid is very effective for stopping and something that I do feel very comfortable with and I think its very like beginning a spin, other than being alot more forceful. – WetSavannaAnimal Feb 2 '18 at 23:17