The way I think about it is that all the individual atoms of the wheel wants to move in a straight line. The only reason the wheel doesn't fall apart normally when it turns is that the material is strong enough to hold itself together. However as it spins faster and faster it requires more and more strength to keep itself together and at some point it moves so fast that the internal strength of the material is not strong enough to pull itself away from this straight line, which causes it to break.