United States Physics Olympiad (USAPhO) is run by the American Association of Physics Teachers and American Institute of Physics to select the team for representing United States at the International Physics Olympiad (IPhO). The selection process is done through many stages. The preliminary round is known as the "F = ma" contest, then semi-final contest and finally a rigorous training camp at the University of Maryland (previously there used to be a Quarter-final round).
I've compiled the past USAPhO problems ("F=ma" contests, Quarter Finals, Semi Finals) with solutions. You can download the papers here.
Source: U.S. Physics Team.