B737 Captain reported a main gear tire failure during the take off roll at rotation speed. The crew continued with the takeoff and continued to the destination allowing the flight to burn fuel as well as conduct a landing with better weather.

Narrative

On takeoff at approximately 170 KIAS at Vr; the left main landing gear inboard tire failed. We noticed a loud bang and a vibration during the rotation. We continued the rotation and raised the gear after the vibrations stopped without issue. I informed Tower we may have blown a tire on the Runway. Tower confirmed there were parts of our tire on the Runway. We coordinated with maintenance control and dispatch and decided to continue to ZZZ (our planned destination) to burn off fuel; for better weather (thunderstorms in ZZZ1) and to have a lower approach speed. I coordinated with the FAs to prepare the cabin for evacuation just in case prior to our descent into ZZZ. I [requested priority handling] with ZZZ Center. We flew an ILS to a 40 Flap landing on XXL in ZZZ without issue. I stopped the aircraft straight ahead and had the fire department verify the aircraft was ok. After confirming everything was ok; maintenance towed us to the gate where we deplaned the passengers normally. Dispatch and Chief Pilot were verbally debriefed.