How should I repair a new crack in the ceiling drywall?
Consider using a paintable latex caulk. Apply a very small amount then work it into the length of the crack with a finger. Wipe off all excess with a damp rag or sponge, then paint. It is a good method requiring no sanding. If your ceiling is painted with flat (no gloss) paint, as most are, you will not be able to see it when you are done.