Originally Posted by
jblackmd
Yes, it is the smallest cog in the cassette, and it does look more worn than the others. I was thinking along those line myself. When I think about it, I do spend more time in 10th gear (the hardest) when on a flat when I have my pedal speed going where I like it. I was thinking that the cassette needs replacing.
It's likely a mismatch between new chain and worn sprocket. If the wheel is original to the bike, it will have a freewheel, not a modern freehub/cassette, and probably only five sprockets. Individual sprockets will be hard to source and not worth the effort. Such freewheels are still available, and not expensive, and will have modern tooth profiles for better shifting performance than the OEM freewheel.