The Arizona State Capitol statue on the top of the rotunda is actually a wind vane and spins around with the wind. I had no idea until I actually saw her move and face me when a breeze came through.
She is named Winged Victory and appears to be modeled after the Greek goddess Nike. <a href="http://www.tigerleaf.com/statecapitols/wt-statue-fe1.htm">This website</a> says that in the early 1900s, people would shoot at the Arizona State Capitol statue just to see her spin around. Those must have been simpler times.