I bought a basic wheel set for a hack bike project. The rear wheel has a single speed cog, and a dangly adjuster thingy - maybe 2 inches long. What is that for?
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The dangly adjuster thing is most likely the toggle chain for an internally geared hub!
The tension on that chain shifts the hub internally (rather than through a derailleur and cogset). Bike hacks with three-speed hubs are quite common, but get very complicated. Here is some information on Sturmey Archer hubs courtesy of Sheldon Brown.
Below is a picture of the toggle chain and rod which is attached to the inside of the hub. Good luck!
It sounds like you have a coaster brake (operated by pedalling backwards), if this is the case then the dangly thing is the reaction arm.