You’ve certainly seen this behavior from your cats at least once. Sometimes they roll on their backs because of catnip, and sometimes they do it for seemingly no reason. This is Kali on our (old) kitchen floor, and she had no catnip anywhere near:
So what’s up with this? Vetstreet says that one explanation is that this is a cat scratching her back. Cats might be flexible, but they can’t reach every itch with their hind feet, and this might be easier than going after it with her sandpaper tongue and needle teeth. That could be especially true if it’s one of those itches that just feels like it’s everywhere at once.
For un-spayed females, this can also be post-mating behavior. Kali, however, is spayed, and has never mated anyway, so that’s not the case here.
Some cats do this as a submissive behavior, and some cats do it when they’re inviting play. And sometimes, says Vetstreet, cats do it because it just feels good. It feels good the way we feel when we have a really good stretch.
We think Kali does this, though, because she gets “rewarded” for it. She did it, we fawned over her for it, and so she learned it was a great way to get attention; the fawning was a form of approval. So, when she wants attention and she’s not getting it, she will sometimes throw herself down on the floor.
(My apologies for the poor quality of the video. I shot this with a really old camera.)