CE-182 pilot reported they inadvertently took off with the tow bar still attached to the aircraft which caused the nose wheel to be severed from the airplane. The pilot continued to destination airport and landed resulting in further damage to the aircraft.

Narrative

I flew my Cessna 182 from ZZZ1 to ZZZ; a private grass strip located approximately XX miles SSE of ZZZ2. The purpose of the trip was to spend time with my son. Upon landing I put the airplane in the hangar; where it stayed until departure at approximately XA:00 for a return to ZZZ1 to have dinner with my daughter.Although the weather was severe clear it was very hot so prior to departure I checked weather for any pop-up TS. There were none. Since it was 95 degrees outside; I did a complete preflight in the air-conditioned hangar; checking oil; tires; surfaces; etc. My son was with me.Upon completion of my preflight; I went to retrieve my bag and briefcase while my son opened the hangar door and moved the airplane to the end of our taxiway. I walked out to the airplane and put the gear in the backseat. I gave my son a hug while standing under the shade of the wing and got into the airplane. I did not do another walk around.Start up and the short taxi were normal. At the end of the runway; I did a runup and completed the pre takeoff checklist. Everything completed; I started my takeoff roll aware of the high-density altitude because of the heat. Everything was normal as I passed V1 and began to lift the nose. At that point I heard a loud bang and vibration. I assumed I had hit an obstruction. The controls were functioning; and the airplane was stable; so I continued my climb to clear trees at the end of the runway.At 1;000 feet I reduced power and began circling to troubleshoot. I was able to get my son on the telephone who told me the nose wheel had been severed from the airplane. Apparently; he had not removed the tow bar when he moved the airplane from hangar and when I rotated it jammed into the turf resulting in the failure. After one more orbit I rejected going to ZZZ2 because of a concern for lack of emergency facilities. I also wanted to try and contact Person A; a pilot and mechanic who also is an expert on my airplane. The airplane was stable; oil pressure solid and controls functioning normal. After talking to Person A; I decided to continue on to ZZZ1 and land on its X;XXX-foot-long Runway XXL. I contacted ZZZ approach; [requested priority handling] and told them my situation. I was cleared into the Class B direct ZZZ1. I transferred to ZZZ1 Tower and told them my intentions and asked for equipment to be standing by. Once I had the runway made; I pulled the mixture; turned the fuel selector to off; turned the master off and turned the mags off. I used soft field technique; touching down on the mains at about 45 knots and holding the nose off until I couldn't anymore. The airplane settled and skidded less than 50 feet. I double checked that the airplane was secure and exited; greeted by the local fire men.There was no fuel or oil spill nor any debris on the runway. The airplane suffered a prop strike and lower cowling damage but was removed from the runway in about 30 minutes.The incident could have been avoided with a simple; final walk around the aircraft after having 'ground personnel' (my son) move the airplane out of the hangar.