C172 pilot reports propeller and engine failure with extreme vibration just after lift off. Aircraft is successfully landed in the runway remaining.

Narrative

I completed a normal preflight check of the aircraft as I was taught with a checklist; and I noted nothing unusual. The subsequent taxi and run-up were normal; with nothing out of the ordinary noted. Airborne after takeoff; I heard a loud bang; saw something out of the upper right part of my eye (in my peripheral vision); and felt severe vibrations in the airplane. I immediately noticed that part of the propeller was missing; and the propeller was windmilling. I landed straight ahead on the available runway remaining. There is no other damage to the propeller; other than the part missing. Additionally; there is some fiberglass damage to the front of the cowling. Callback conversation with Reporter revealed the following information: The Reporter does not believe that the engine actually failed as it was still running after the aircraft was brought to a stop. Continued flight was never a consideration though due to the extreme vibration. The engine was shut down on the taxiway and the aircraft was towed to its spot. Post flight revealed that a two foot section of one propeller blade had departed the aircraft and the remaining blade was intact and undamaged. No cause has been determined at this time.