The only thing that’s valid (and I didn’t really understand if the video maker understood it bc he wastes so much time on the wobble) is that if you spin sth up to, say, 200 /s, then your rocket will spin, with its full length, at 200 /s. I don’t know how they want to address that.
I clearly see their rocket rotate around its center of gravity, with the same angular velocity as the arm it's sitting on, while the center of gravity is moving on a circular path.
So, again, how is it not spinning? Where does the angular momentum go?
No, the better question is where it came from. The launcher spins the payload like a bucket on a rope. So upon exiting the launcher it isn't spinning. But by setting the guide vanes at a slight angle the payload can be made to spin to give it more stability (since this is essentially unpowered flight for the first bit) and it can be de-spun in the same way.
The launcher does not spin the payload around the long axis.
I can tell you exactly where it came from, it's being spun up in that launcher thing, obviously, that's the whole point of spin launch. You can see it for yourself in the video. Is the pointy end of the rocket always facing in the same direction, e.g. upwards? No, it's changing its orientation continuously, it's always facing 90 degrees from the arm of the launcher, which, you guessed it, spins.
It is indeed exactly like a bucket. And the bucket changes its orientation throughout you spinning it, that's the whole thing, that's why the water stays inside. The top side of the bucket is always facing you. For that to happen, it has to rotate around its COG with the same rate it's rotating around.
A different example: the moon is tidally locked to the earth (like the bucket to you, or the rocket to the spin launcher) - very obviously, it needs to spin around its axis to achieve that, and it does so at exactly the same rate as it is rotating around the earth.
