My 17 Elantra sport in currently at the dealer for the second time with the same issue... when the tire starts to rotate, it begins to make a metal grinding noise. (I already had the rotors and brake pads replaced under warranty)
I just noticed a similar issue the other day after making a run up and down Mt Lemmon in Tucson. I also noticed under trail braking and turning that I got a vibration through the brake pedal. Going to have to do some inspecting.