Using centripetal force puts it in trebuchet territory does it not?
Ignoring air resistance (which you really shouldn’t, especially not when you’re talking in the thousands of meters per second), you need to launch something at around 1400m/s get it to 100km high “suborbital”. You need to launch it over 8000m/s to get it into orbit. In 2022, Spinlaunch were getting to ~450m/s, but that was two years ago and maybe they’ve improved.
Now, 1400m/s is in the neighborhood of a tank cannon, which is doable. But 8000m/s on the surface, or about 29.000 kph, is about mach 23. That’s like running smack into a brick wall of air, every millisecond. And in reality, you need MUCH more speed, because you’re shooting at a much shallower angle, so there’s a lot more air to get through.