My 11 year old is learning to use my rotary cutter now. She's been allowed to use my computerized sewing machine and iron unsupervised (with permission) for a year now, and my older machine (it's mechanical, not computerized) for about 2. She started sewing by machine when she was 8, but was only allowed to sew while I was in the room then.
Next she gets to quilt her current project on my frame- with assistance, of course. She is entering it in a quilt show next spring, and the requirement is that she does all the sewing herself. I did help her with the cutting up until this last stage, though, which was within the rules of the youth category.
*Edit- I do have 2 rotary cutters: one has a guard of sorts, so your hand cant slide onto the blade, the other is less, shall we say, idiot proof. She's not allowed to use the 2nd one, and she knows it.