Okay, so there's something I've been trying to puzzle out, and after quite a bit of searching around I've only found almost-but-not-quite answers. And since I'm a chemist, not a physicist, even my Newtonian-fu has degraded catastrophically since uni.
Imagine there's an astronaut, in a spacesuit, strapped to the wall of a spaceship where things have gone terribly wrong. A hull breach has sucked all the air out, so there's just the vacuum of space inside, and the ship is spinning wildly on its axis. The astronaut manages to unstrap themselves, and then launches themselves (let's say with suit-boosters of some kind) from the wall, directly forward - so, in the direction of the center at the moment the force is applied.
TL,DR: object attached to, and then pushed away from, a spinning frame in a zero-G vacuum.
Since there are no gas molecules of any kind to interact with, and if we pretend for a moment that the "push"-velocity away from the wall is achieved instantaneously (zero-to-whatever in no seconds), is it correct to assume that the total velocity vector after breakaway is just the sum of the angular velocity from the spinning frame and the "center"-directed velocity? As in the embarrassingly crude picture below, with red "spin-vector", yellow "push"-vector, and orange "sum"-vector?
And of course there's going to be coriolis effect, because the astronaut won't be spinning the moment they detach from the surface, while the frame keeps rotating?
Extra wrinkle: If the straps holding the astronaut aren't completely taut, say, a couple cm of slack, will the astronaut still be pulled in tight against the wall, and would they be pulled as far towards the direction of rotation as the straps allow?
Apologies if some or all of this makes no sense, if it's embarrassingly wrong, and for almost certainly missing some obvious, better, scientific terms I could've used to make things clearer. And for making it so damn long.