C150 Flight Instructor reported loss of the propeller spinner after rotation which caused banging; vibration and an apparent partial power loss. Instructor returned to departure airport and found minor damage to the propeller and cowling.

Narrative

Just after rotation and during climb out from Runway XXR while on an instruction flight with an Instrument student; there was a loud banging and impact to the front of the Cessna 150 resulting in vibrations and apparent power loss while climbing through 500 ft. (350 ft. AGL). I took controls and immediately initiated a turn back towards the airport. Also; I reported to ATC we were 'Coming back.' We were cleared to land any runway and made a downwind landing approximately half way down Runway XYL. Power loss was suspected but during the execution of the turn; I noticed the throttle was retarded by the student at the moment of impact. I was able to use normal power to stabilize the approach prior to landing. Upon roll-out; Tower reported the spinner was missing on the [Cessna] 150. After stopping off the runway; we found the spinner had separated from the propeller hub and had struck the prop as well as holed the upper and lower cowlings. No oil or fuel leakage was found. No damage to persons or property (beyond the minor damage to the 150) was found. The remnants of the spinner were found at the departure end of Runway XXR. Tower requested a phone call and we called with details and reported the same minor damage to the aircraft and instructor's contact details.