It matters to understand the question before you can think about the answer. That's why I asked you to specify the situation.
From your answers to the other comments It seems that you think that the speed of the ball has some influence on its internal energy, resulting in the ball evaporating and so on. This is not the case, as it was already mentioned. However none of your scenarios are good illustrations for this scenario.
A spinning ball, made from real materials will break into pieces at speeds way below the speed of light. This has nothing to do with relativity. It's just that the bounds between the atoms or molecules of the solid can sustain only that much centripetal force and as the spinning speed increases more centripetal force is required.
For the orbital motion of the ball, a similar problem will arise. If the ball moves faster either you need a larger trajectory or an increased centripetal force. In order to have circular motion you need some attractive force, like gravity. So in a very remote area of the universe, in absence of other bodies, what will make your ball go in a circular trajectory, anyway?
You see, if you want to discuss the effect of relativistic speeds alone, on an isolated body (in a remote area), you should choose a situation where the body moves in straight line, to eliminate the need for forces. This is the only type of motion for an isolated body. And in this case, there will be no reason for the body to change the state in any way.