The pilot reported that prior to takeoff, he removed the left main landing gear wheel because its tire had a slow air leak. The pilot, who holds an airframe and powerplant mechanic certificate, reported that after replacing the tube he reinstalled the wheel on his airplane. He indicated that when performing this maintenance, he did not properly secure the wheel’s retaining nut with a cotter pin. During his subsequent takeoff roll, the attachment nut unscrewed, and the wheel separated from the axle and airplane. The pilot flew around the area for about 30 minutes burning off fuel. Upon landing, the airplane veered left off the runway and nosed over, breaking wing ribs and a lift strut.