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:
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.)
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.)
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.