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Ah, yes, but/t, the atoms in her lower arms have a forward momentum.All parts of her have angular momentum in the same direction, which I suppose by definition must be 'forward'. Assuming she's spinning counterclockwise as viewed from above, her angular momentum including her arms and other parts) have an angular momentum vector pointing up, not some other way. Fold the arms inward, crossing to the other side and their angular momentum is still up, but less, having transferred some of it to the torso. The direction of the momentum never changes no matter what contortion she puts herself into, including inverting, legs up. Angular momentum remains up the whole time.
Her leading edge is now her trailing.There is no leading edge to rotation. That's a linear momentum trait, which is also conserved, but the spinning skater doesn't have much of that in the frame of the ice into which she's eroding a hole.
What's the Coriolis force got to do with it? Never thought about that.It's what makes hurricanes do the same thing: spin faster when the air draws inward like the skaters arms, due to the low pressure center at the middle. It's what makes you pee in a curved path while standing on a rotating space station. It happens on Earth too since it rotates, but few pee far enough to notice the curvature.
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