I did focus attention on the fingers, which follow the direction of rotation. The thumb is just a good way to keep track of which way the fingers are going. It’s the rotation that has inertia. Your hand is just being used to keep track of the direction of rotation.
“Physics cannot explain why, only how” - Richard Feynman.
Why is angular momentum conserved is a major philosophical question beyond the scope of this discussion, unless you’d like to bring us down that tangent? We could talk about Noether’s Theorem, and the nature of rotational symmetry. I just don’t think that starting from “the laws of physics contain an azimuthal symmetry from which a law of conservation of angular momentum can be derived” is the right vibe here, and it only pushes the unanswered “why” into the symmetry of our equations instead. OP wanted the how, not the philosophical why.
I’m sorry but this answer is not wrong, it’s just not an answer.
You are not explaining the reason why, you are explaining how to solve it using some useful tricks.
Physics doesn’t act according to your thumb and surely your thumb does not encapsulate the essence of inertia.
It’s akin to answering “What is 2 x 3?” and answering providing a table where to look up the answer for each combination of number to multiply.
I did focus attention on the fingers, which follow the direction of rotation. The thumb is just a good way to keep track of which way the fingers are going. It’s the rotation that has inertia. Your hand is just being used to keep track of the direction of rotation.
“Physics cannot explain why, only how” - Richard Feynman.
Why is angular momentum conserved is a major philosophical question beyond the scope of this discussion, unless you’d like to bring us down that tangent? We could talk about Noether’s Theorem, and the nature of rotational symmetry. I just don’t think that starting from “the laws of physics contain an azimuthal symmetry from which a law of conservation of angular momentum can be derived” is the right vibe here, and it only pushes the unanswered “why” into the symmetry of our equations instead. OP wanted the how, not the philosophical why.