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Wonder if the result would be different if you could somehow get the force applied evenly across the surface.
Answer: not really, no.
What you're seeing is the result of centripetal acceleration or centrifugal force or whatever physicists feel like being pedantic about. As an engineer, all that matters is that there's a force which is pushing uniformly outwards on the wheel, which results in two types of stresses: radial stresses (which act normal to the surface of the wheel) and hoop stresses (which act tangent to the wheel). This is basically an analysis of a thin walled pressure vessel minus the longitudinal stresses.
The waterjet provides the rotational velocity which generates the centripetal acceleration, which creates the predominately hoop stresses in the wheel. These hoop stresses are orders of magnitude greater than the minor radial stresses, which are presumably what you're imagining changing the deformation mode. So changing to another method of force application won't change the end result: hoop stresses accumulate from rotation until the tensile forces exceed the strain limit for this (presumably hyperelastic) material.
TL;DR, the end result is the same because the global forces generated by the rotation are far greater than the local forces generated by the waterjet.
It would flatten out against the surface and then break similarly but out to the sides
Yup, looks like it breaks because the string essentially cuts it in half
Watches 10 seconds gif "yeah, I know exactly what's going on here and will confidently state my incorrect opinion as fact"
But... You can see a divot in the center of the wheel where the string is making contact. It looks like it breaks apart because of that new weak point. It's not like I'm being an armchair physics professor, I'm making an inference.
What string? It's a water jet.
You know, I wasn't sure whether it was a water jet or not, since that's used to cut through STONE. So, it's likely that the wheel was being cut in half prior to it tearing apart.
The ones used to cut through stone and steel typically have diamond "sand" muddying the water. At least the one at my local machine shop does. I'm guessing the one in the gif is straight water.