So, what do I need to know about using an angle grinder as a cut-off tool? Are some disks better than others? Certain disks for certain types of metal? What made mine fly apart? Is heat an issue? It didn't seem to be that hot. Is it common for them to come apart?
I use cut-off discs all the time on steel. I use Harbor freight (sometimes 80cents each) and name-brand ($4 each), and find that the Harbor freight work fine, and last fine too, and there's not a noticeable difference. There are thinner wheels too (.040") that are useful to have around, and some have an offset in the hub, which is nice for flush-cuts. The HF discs are about .060 thick. I use them for light grinding too, sometimes cutting welds, or grinding out tacks. I like them and consider them a valuable tool.
It has a lot to do with how you hold the grinder. Sorry I can't explain this better, but if the disc "chatters"; the disk is wearing away quickly. Actually it's chipping away. You MUST choose the direction you are cutting, and the center of the cut in relation to the spin axis, such that it does not cause the grinder to oscillate. Sorry this is hard to type, and even hard to demonstrate, because nobody wants to dempnstrate a chattering disc. Maybe someone else can explain better than I.
If it starts to chatter, stop and look at the disc, often it's frayed and un-even, not round. I've been able to heal a disc if it's less than about 1/4" out of round. If you crack/break the disk (by dropping the tool etc) then throw it away, that chunk will fly off at 10,400RPM.
These cutoff discs are not for everyone. As mentioned above, if the item you cut, pinches on the disc at the end of the cut, it can be a problem. You have to be careful.
Heres a pictorial example of using the cutoff disk. This motorcycle footpeg mount was cut off with a harbor freight disc on an angle grinder. Also the replacement part (1/2" steel) was cut entirely with one HF disc. (The photo of the 'intact' footpeg mount is the 'other side'). I did the minimum work required (that the owner couldn't do) left him to finish it out to his satisfaction. And he did, all good!