If you're wondering, this is one of the epic, legendary practical effects: the room itself rotated, and the camera rotated with it.
And here's the full clip, with the music (and Mr. Astaire singing):
Even if he were dancing on a stable floor (that wasn't rotating under his feet), his dance moves would still be breathtaking.
Impossible not to watch this in complete fascination, both at the practical effect's amazingness and Astaire's utter mastery.











