MD-82
Flight Crew Air Transport Pilot (ATP)
Aircraft Equipment Problem Critical; Flight Deck / Cabin / Aircraft Event Illness / Injury
Flight Crew Inflight Shutdown; Flight Crew Returned To Departure Airport; General Declared Emergency
Aircraft
On takeoff at ZZZ; after V1; we felt vibration in aircraft; immediately followed by strong burning rubber smell. As the co-pilot rotated aircraft; I monitored engine instruments and noticed left engine severe power loss; followed by engine regaining power. I announced to the First Officer I believed he might lose number 1 engine. This was immediately followed by multiple severe compressor stalls. Declared emergency with ATC. At engine out altitude; performed QRH procedures and shut down left engine. After landing; rescue crew inspected aircraft; and I had aircraft towed to the gate. On final turn in to the gate under tow; a flight attendant advised of a medical emergency in the aft cabin. I called for paramedics and had the ill passenger treated and removed before other passengers disembarked.
[The report narrative contained no additional information.]
When; after V1; debris from a failed main gear tire was ingested by the left engine on the takeoff roll a significant power loss and compressor stalling resulted.  The engine was shut down in flight and the aircraft returned to the departure airport.