Removing rust from bicycle components

Recently brought home a free bike I found posted online, however after some of the snow melted from it I found out that the chain stay on the non drive side had burst due to water freezing inside. I immediately asked the bike gurus at /r/bikewrench on what to do and to my dismay it turns out the frame can no longer be salvaged and must be discarded as it is unsafe to ride. I wouldn't really want to be riding that thing when the chain stay finally gives up and break!

That was a major bummer, however all is not lost as I was able to salvage some pretty good parts from it.

The Giant Cypress that wasn't meant to be.

That's a pretty big hole!

The front and rear derailleur looks pretty good but a bit rusty, the brake and shift levers were the same ones that I just recently purchased from Recycle Cycles to replace my old mountain bike shifters.

So on my way home from work I bought a can of Rust Check, seeing as there seems to be a lot of online post that says it works and also got some steel wool at Canadian Tire.

Sprayed a decent amount of Rust Check on the corroded parts and left them there for a couple of hours, the finally used the fine wool to scrub off the rust. All I can say is that I'm pretty much satisfied with the results, I probably would need to clean the derailleur on the mtb once my new work stand gets here.