No, it's exerted in this case by the wall behind you keeping you from flying away. If you were on a string attached to the center, it would be the string exerting the centripetal force. You keep going off on tangential paths, but the wall is there and shoves you back toward the central point. every instant. Inertia and friction and gravity are what keep you in place on the wall as the machine accelerates.
Old men, fear me! You will shatter under my ruthless apathetic assault!
Uschi - 2 Old Men - 0
"I am convinced that this world is of no importance, and that the only people who care about dates are imbeciles and Spanish teachers." -- Jean Arp, 1921
"If Jesus came back and saw what people are doing in his name, he would never never stop throwing up." - Max von Sydow, "Hannah and Her Sisters"