spin has 10 distinct synonyms spread across 5 of its 13 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
stream in jets, of liquids
“The creek spun its course through the woods”
form a web by making a thread
“spiders spin a fine web”
work natural fibers into a thread
“spin silk”
a short drive in a car
“he took the new car for a spin”
a distinctive interpretation (especially as used by politicians to sway public opinion)
“the campaign put a favorable spin on the story”
Synonyms, antonyms and the broader and narrower relations for spin come from Princeton University’s WordNet. Full sources and licences.