http://en.wikipedia.org/wiki/Centrifugal_force
a = v^2/r
so let's go with 1km/sec and a diameter of 5m. a = 1,000 x 1,000 / 2.5 = 400,000 m/s^2 or roughly 40,000 g
Now let's assume that it's a 1/4lb weight as described or 0.1kg.
F = m x a = 0.1 x 400,000 = 40,000 newtons.
Next let's assume that the piece of metal is steel and roughly cubic. It's density is around 8g/cm^3 (http://hypertextbook.com/facts/2004/KarenSutherland.shtml).
Mass = density x volume => volume = mass / density = 100g / 8g/cm^3 = 12cm^3
cube root(12) ~= 2.3 so we've got a cube with faces around 2.3cm on a side.
They've said that they're going to encase it in plastic so let's neglect the strength of the plastic and call it 2x the size of the cube. That brings this to 5cm x 5cm.
Now let's translate that into pressure.
P = F / a = 40,000 / (.05 x .05) = 16 MPa
The tensile yield strength for a regular, boring steel (A36) is 250MPa and the ultimate tensile strength (the max it can hold prior to breaking but after deforming) is 400MPa so this is fine for now.
http://en.wikipedia.org/wiki/Ultimate_tensile_strength
At 2km/sec you get 64MPa needed and at 7km/sec you need 784MPa all of which are within the realm of possible but rapidly heading towards the limits of material strength.
The 784MPa number would go down if you made the diameter bigger, too.
Ultimately they aren't building a thing which will disintegrate the slug (my initial thought) but it's going to have to be extremely well engineered and precisely made for balance in order to ensure that it doesn't tear itself apart. The technical combination of a steel rolling mill and a swiss watch. And due to balance issues definitely harder from a technical perspective than even the really tough portions of a rocket.
EDIT: didn't realize that "*" did formatting so I fixed it.
EDIT2: Screwed up on the calcs, assumed 10,000m/sec instead of 1,000/msec. Fixing those.