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The way I understood it (probably wrong): imagine if a point like thing, but is actually a wave, hits something else. It will leave a trace on the detector curving in a certain direction. This is interpreted as angular momentum aka spin.
There are also things like Hydrogen Fine Structure , that behaves as though it is a ball that actually spins. 🤷
…that is f*cking brilliant…
You must be thinking of the Stern-Gerlach experiment.