[Curious Cat (OP)]

.

[Bored chemist]

https://en.wikipedia.org/wiki/Coriolis_force

[alancalverd]

Nothing is going the wrong way. For some reason I always imagine myself spinning anticlockwise viewed from above, so every off-axis atom is moving anticlockwise. Now I alter my moment of inertia by extending or contracting my arms, angular momentum is conserved, various  atoms move faster or slower, but still anticlockwise.

[alancalverd]

I think I can see the confusion.

Spinning anticlockwise with arms outstretched, if you cross your arms forwards and all the way across your body, your right arm temporarily rotates a little quicker and your left arm a little slower, but there is no net change in angular momentum and the whole lot continues to rotate anticlockwise.

Not to be confused with spinning an airplane, where the outer wing speeds up and the inner wing slows down with respect to the airflow and becomes stalled. If you really screw up, you might even get part of the inner wing to move backwards, with truly  disastrous results.

[alancalverd]

t's what makes you pee in a curved path while standing on a rotating space station.

Ah yes, we've all observed that. Bloody nuisance, having to review rotating differential geometry after a few beers.

[Petrochemicals]

How does a spinning skater really work?

Suppose she starts out with her arms straight out, brings them in by
bending them at the elbows, horizontally, and speeds up, and yet those
atoms in her lower arms are now "pointing/going" the wrong way,
to the direction of motion, if U get/know what I mean!?

Yes but the skater is one cohesive bundle,

[Colin2B]

Yes but/t is still made up of individual atoms, with a momentum, of their own.
What I'm really saying is: What if she folded her arms very quickly? How would the atoms react, exactly?

The atoms are her arms, it’s the atoms doing the moving.