A B737-300 FLT CREW; ON APCH; SELECTED FLAPS 30 DEGS THEN HEARD A 'THUD.' LNDG WAS NORMAL. MAINT INSPECTION REVEALED R OUTBOARD FLAP SPINDLE FAILED.

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APCHING BNA RWY 2C; 2100 FT MSL (1500 FT AGL); 153 KIAS; GEAR DOWN; FLAPS 15 DEGS; AUTOPLT ENGAGED; WE SELECTED FLAPS 30 DEGS. AS THE FLAPS EXTENDED; WE HEARD A 'THUD' SIMILAR TO A NOSE GEAR EXTENDING HARD. THERE WERE NO OTHER ABNORMALITIES. #2 ENG WAS RESPONDING TO THRUST CHANGES SLOWER THAN #1; SO I WAS NOTICING YAW AND ROLL ASSOCIATED WITH MY FINE TUNING OF THE THRUST. AT ONE POINT AFTER DISENGAGING THE AUTOPLT; I DID HAVE TO MAKE A SLIGHT (10-15 DEG); MOMENTARY L YOKE INPUT. 1 OF MY 2 JUMP SEATERS MENTIONED SPINDLE FAILURE; BUT I DISMISSED IT IMMEDIATELY BECAUSE; 1) THERE WAS ABSOLUTELY NO UNUSUAL ROLL OR YAW; AND 2) I WAS NOT AWARE OF ANY COMPANY B-300 ACFT EXPERIENCING SPINDLE FAILURES. I THEREFORE DID NOT PERFORM THE SUSPECTED FLAP SPINDLE FAILURE PROC. WE LANDED UNEVENTFULLY. AFTER LNDG; THE JUMP SEATER INFORMED ME WE HAD EXPERIENCED B-300 SPINDLE FAILURES. AS A PRECAUTION; WE CALLED MAINT AND DESCRIBED THE PROB. THEY DID FIND A BROKEN SPINDLE ON THE R WING. SUPPLEMENTAL INFO FROM ACN 625178: WE ALL WONDERED WHAT THE SOUND WAS. (WE HAD 2 COCKPIT JUMP SEATERS.) THE CAPT THOUGHT IT SOUNDED LIKE A LATE GEAR DEPLOY. THE JUMP SEATERS AND I DIDN'T THINK SO; SINCE WE HAD BEEN SHOWING 3 GREEN WELL BEFORE THE POP. WE MENTIONED SPINDLE FAILURE; BUT DISCOUNTED SINCE THERE WAS NO ROLL-OFF. THOUGHT IT WAS PROBABLY A BIRD AND WE WOULD MAKE SURE THE ON-COMING CREW DID A GOOD INSPECTION. TAXIING IN WE DISCUSSED WHAT THE NOISE COULD BE. AFTER DISCUSSING; WE AGREED IT SOUNDED MORE MECHANICAL THAN BIRD STRIKES WE HAD EXPERIENCED IN PAST. WE DIDN'T THINK SPINDLES WERE AS BIG OF AN ISSUE IN THE B-300 AS OPPOSED TO THE B-200; BUT KNEW IT COULD HAPPEN. ONE OBSERVER HAD JUST RETURNED FROM TRAINING AND SAID THAT COMPANY HAD A FEW SPINDLE FAILURES IN B-300. MAINT DID A SPINDLE CHK; AND DISCOVERED THE R OUTBOARD SPINDLE BROKEN.