The mass of a proton at 7 TeV is about 7,460 times the mass of the proton at rest. My guess is that the mass of particles being brought up to speed is on the order of grams per day, maybe pounds. I don't know how much "rest mass" is involved in each collision, but this "supermassive" event is probably like banging a pair of 1 pound weights together, at most. Hardly enough to affect the earth's rotation.
LHC machine outreach FAQ has the "energy to mass" calculation.
Ha...there you go, assuming that today’s science is correct. What if much of what you are saying is eventually proven wrong? That is what makes Science so much fun...
So then,
it’s NOT TRUE that things approaching the speed of light are similarly approaching infinite mass?