Sounds like this solves the easy part (getting to high altitude), but makes the hard part (getting to orbital velocity) even harder.
This thing is going to tear itself apart as soon as it leaves the centrifuge.
If they could just launch at 45 degrees to get to orbit the rockets would do that too, but no they don't. They go straight up at first because the drag is such a huge penalty to the performance.
If they actually build this thing, the most efficient way to launch is to launch it almost straight up at 90 degrees so they lose the least energy. However the hardest part is going to be immediately after exiting this thing where they hit the atmosphere going mach 6-7 and instantly turn into a glowing ball of plasma, which is what happens if you try to move that fast at sea level.
Drag forces increase with the square of the velocity and linearly with fluid density. The instant it leaves the cannon it will feel like it's hitting a brick wall.
If I understand correctly, this would hold for angular acceleration too, since they'd just release at some point. Can someone correct me if I'm wrong?
Take a 200 pound payload, add some rocket to it, let's say 10x the weight to be generous, then spin it in a circle 200 feet in diameter. You're looking at 18 thousand tons of force spinning it at 5000mph. So you're spinning 4 navy destroyers worth of force in a circle, which means you need a latch mechanism that can not only hold that much force, but release it at the exact moment to exit the biggest vacuum chamber ever created through a door that just opened at the right time, generating a mach 6+ shock wave at about 0 meters distance from the door and somehow not destroying it in the process. I don't know that it is impossible, but it is highly improbable. They'd probably have a burst disk rather than a door, because that would let you use the capsule as a bullet to penetrate the exit.
In the article they mention the payload experiencing 10000g, so they must be planning on a circle greater than 200 feet in diameter. I can't find numbers on existing satellites, but I remember reading that rockets typically top out at 6g acceleration and figure on a 10x momentary acceleration due to vibration. To tolerate 10000g the payload being launched will need to be built like a tank, rather than the relatively light current designs. To ease that requirement you could submerge the payload in liquid, but that would decrease your usable payload accordingly.
It would be impressive if they could actually pull it off. I think it would be useful for limited applications. I have watched science fiction shows where mass accelerators could basically nuke planets without radioactive fallout. Maybe this would be something similar.
And just for a sense of scale, escape velocity from earth's surface--assuming no atmosphere at all--is 25,000 miles per hour. The projectile is going to tear itself apart in atmosphere at those speeds.
Centrifugal projectile weapons scale up poorly and have issues even at BB gun scale. Envisioning what happens with a 200lb projectile; leave aside the laughable velocities they're talking, and I want to be well distanced from these people when they power shit up.
I think this is a device for separating investors from money.