A student pilot was conducting touch and go pattern operations during her second supervised solo. The pilot said that on the second touch and go she touched down on the runway to the right of centerline after a normal approach. The pilot then added full power, began retracting the flaps, and tapped the left rudder to correct the airplane back to centerline. Suddenly the airplane swerved to the left and the pilot added right rudder pedal but the airplane did not respond. The pilot then added brakes in an attempt to stop but the airplane continued to veer off the runway to the left. The airplane subsequently hit a lip on the taxiway and nosed over, coming to rest inverted. An FAA inspector examined the airplane following the accident and the nose gear steering linkages and brakes appeared normal.