I've had my bike up on a stand to give it a clean. As I was cranking the pedals to clean the chain, then let the pedals go, I noticed that when the back wheel was freewheeling it would start the pedals turning by itself. Why does this happen? I also noticed that if I had the front on the little granny ring, and the back on the littlest sprocket that with the back wheel spinning, not only would it start pushing the pedals around, back there 'e also a fair amount of slack in the chain. What does this mean?
The friction between the bearings, pawls and lubricant in a freehub or freewheel are usually enough to turn the pedals when the wheel is spinning. If you hold onto the pedal and the wheel freewheels normally, probably there isn't anything to worry about.
Of course, if the wheel stops freewheeling altogether or the friction to resist the wheels turning becomes noticeable, then inspect the freehub bearings and pawls. Increased resistance at the freehub/freewheel will often result in the rear derailleur being pulled completely taut when the pedals are stopped.
If the freewheel is spinning, and the pedals begin to spin, the only possibility is that the freewheel is pushing on the crank via the chain, and the chain is being pushed by way of the rear cassette. I would guess that your chain may be stiff in parts (possible if it's rusted in parts), and that the rear hub may have a problem (could either be a bent axle or a failing ball-bearings, or both, from my experience).