In Saturn V launch footage, the interstage ring falls away shortly after stage I separation, briefly catching fire from the stage II exhaust. Does this ring continue to drop uncontrolled and impact with Earth? Does something this large disintegrate completely in the atmosphere?
The first stage and the interstage ring both did fall uncontrolled after stage separation, landing somewhere in the Atlantic ocean. Stage separation occurs at about 2400 m/s and 67km altitude. That's fast enough for re-entry scorching, certainly, but not enough to burn up completely. In 2013, more than 40 years after flight, one of the first stages was found on the ocean floor and an F-1 engine recovered. While the stage was shattered and the engine badly deformed by the ocean impact, it wasn't burned up, and the interstage should have fared similarly.