Sprocket/Free Wheel Sway
 

Hey, I just re-assembled my Fuji after cleaning it, and while tuning the rear derailleur, I noticed that there is some sway in the freewheel/sprocket cone while coasting, as shown in video. http://www.youtube.com/watch?v=H_6760F6Zsg I realize that it isn't the clearest, but if you look close, you'll see what I mean, especially if you watch the chain, as it is a direct result of that. After doing a bit of detective work, I have found that the problem lies with the freewheel/sprockets, and ruled out the hub or axle, both appear to be alright, and there is no play between either, as the cones are adjusted well. Thank you, any help is appreciated

That is pretty normal behavior in freewheels. I wouldn't worry about it.

+1, Freewheel wobble is perfectly normal, and has been for 50 or more years. I could explain why it happens, but it's been asked and answered so often that a fast search will bring it up.

If you do a search here or on the internet, you'll find that this one of the most common questions, after the one about the broken or missing chainring teeth on new bikes.

Looks fine to me.

+100. Back when all bikes had freewheels (and dinosaurs roamed the Earth), they all did that. Better freewheels wiggled less, but they still wiggled.

Freewheels are not built to such high tolerances that they don't wiggle a bit.

http://www.youtube.com/watch?v=OI6JxL-zjXc

...explained.

=8-)