Our friend <PERSON> can help us here with his equation of circular motion:
$F = \frac{mv^2}{r}$
where F is the force produced, m is your object mass, v is your object's linear velocity, and r is the radius of motion. As you can see, it's the speed you want to reach that is going to have more of an impact than your mass (which, by the way, is still a problem).
Based on your numbers, you'll be subjecting your accelerator to 6 billion Newtons of force. This will likely cause it to break into tiny pieces. By the way, 30km/s is Mach 88 (88 times the speed of sound). This rotary force is enough to fling New York City into space- you must have some interesting needs.
Running your cannonball at Mach 1 (340 metres per second) will still put a big hole into whatever you fire it at. You'll put 771,000 Newtons of force onto your accelerator, which at a big enough scale it should be able to handle.
On a final, more interesting note, the velocity of an object in a circular path acts at a tangent to the circle, but the acceleration (and thus the force) acts towards the circle's centre. As the direction of velocity is constantly changing in a circle, any object in circular motion is accelerating with this force. Something to consider in your designs.
EDIT: Have you considered modelling the projectile as a point charge in a magnetic field, and accelerating it radially?
My maths may need some touching up here, but using the equations for magnetic flux density we can see: $F = BQV = \frac{mv^2}{r} $
where B is the magnetic field strength, Q is the value of the point charge passing through the field and V is this charge's velocity. Using this, we then get:
$ BQ = \frac{mv}{r} $
Plugging your numbers back in, it turns out that the product of our magnetic field strength and charge of the particle needs be 200,000 Tesla Coulombs. 780
Teslas are harder to increase than Coulombs due to their exponential nature, so lets keep those low. We can already produce up to 45 Teslas, so let's say we can produce 50 on your spacecraft. This means your projectile needs a charge of 4,000 Coulombs (which is still a lot), but assuming you keep it in a vacuum and it's perfectly spherical, you can use <PERSON>' Laws to calculate the current needed to be held in the projectile and the distance it needs to be from its enclosing magnets to reach this exit velocity in a certain time.
Without number crunching myself, it doesn't look so bad. Plus, with magnetic confinement the force of your projectile is meaningless as it's not actually producing a net force on any surface connected to your ship.
EDIT II: Electric Boogaloo
As suggested by @Efialtes in the comments below, this system would require a ridiculous amount of energy. By substituting in
$ E_K = \frac{1}{2}mv^2 $,
we can calculate the projectile's energy is 0.45 TeraJoules. I cannot begin to quantify how huge this is.
Further, the field would have to be able to shift one million kilograms every five seconds to produce this power. Using equations for electrical energy (and assuming the device is 100% efficient), running this device for ten seconds would require a terawatt of juice. If you prefer, we can assume this device has an internal resistance of 10,000 Ohms (which would be very low). I can then tell you this would need a continuous supply of 2.08 MegaAmps. It takes one MegaAmp to fuse together atomic particles in a superheated plasma, so I really don't envy anyone tasked with designing something like this. 921