ACR MLG SHEDS RECAP OFF ONE OF THE ACFT'S NOSE TIRES DURING TKOF PROC IN LOW LEVEL WIND SHEAR CONDITIONS.

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WE TAXIED TO RWY 35R AT DEN FOR TKOF. IT WAS THE ONLY RWY WITH EXCEPTION FO RWY 35L DUE TO OUR TKOF WT BEING 1500 LBS BELOW GROSS TKOF WT. WINDS WERE VARIABLE 280-260; 25 GUSTING TO 37 KTS. I TOLD THE TWR CTLR WE COULDN'T ACCEPT TKOF WITH ANY GUSTS ABOVE 29 KTS. WE WAITED AND AFTER A COUPLE OF MINS DEN TWR RPTED A WIND 280 DEGS AT 28 KTS. I ACCEPTED AND HE CLRED US FOR TKOF AND ISSUED A WIND SHEAR ADVISORY FOR 15 KTS ON DEP. THE FO WAS FLYING AND I GAVE HIM THE AIRPLANE AFTER RWY ALIGNMENT. IT WAS A MAX PWR TKOF. AFTER PWR WAS SET; I TOOK THE THROTTLES IN MY HAND. OUR CALCULATED V1 SPD WAS 160 KTS WITH VR AT 166 KTS. THIS WAS A VMIN V1 SPD. ACCELERATING THROUGH 120 KTS WE HAD A MOMENTARY STAGNATION IN AIRSPD. AT 140 KTS THE AIRSPD JUMPED TO 150 KTS. AT V1 OF 160 KTS I CALLED V1 STAGNATION. THE AIRSPD STOPPED AT 160 KTS FOR MANY SECONDS. I TOLD THE FO TO KEEP THE NOSE ON THE RWY. I HAD HIM ROTATE AT 180 KTS. I RPTED THE SHEAR TO TWR. WE USED APPROX 10000 FT OF 12000 FT OF RWY. I WAS JUST SHORT OF APPLYING FIREWALL PWR. DURING CLBOUT; THE 'A' FLT ATTENDANT TOLD US THEY HAD A STRONG SMELL OF RUBBER IN THE CABIN. WE DID NOT HAVE IT IN THE COCKPIT. UPON LNDG IN CLT; I WROTE THE SMELL UP IN THE LOGBOOK. UPON INSPECTION OF THE ACFT; A MECH DISCOVERED OUR R NOSEWHEEL TIRE HAD BLOWN A RECAP AND THE ENTIRE TIRE WAS TREADLESS DOWN TO THE CORD. I RPTED THE INCIDENT TO OUR DISPATCHER TO ADVISE DEN TWR OF POSSIBLE FOD ON RWY 35R.