Revolving Mezuzot!?

While I stood yesterday at my favorite Jewish-ish diner in the South Loop of Chicago -- Eleven City Diner -- waiting for one of my best friends from high school and her newish husband to arrive for lunch yesterday, I discovered a perplexing question I had no answer to, as I watched people shuffle in and out of, well, a revolving door -- the choice of entryway for many Chicago establishments, to keep the cold in and the heat out. The question?

Do you affix a mezuzah to a revolving door? Is there any responsa about revolving doors and whether it is necessary to affix mezuzot to them?

So, if anyone knows, please let me know. Otherwise, I'll find a rabbi and ask, like the Orthodox community websites for Brandeis and Penn tell me to!