- IN THIS EXAMPLE WE'LL DETERMINE
HOW FAST A CAR TIRE IS SPINNING
IN REVOLUTIONS PER SECOND
IF A CAR IS DRIVING 45 MILES PER HOUR.
LET'S TAKE A LOOK AT THE INFORMATION THAT WE'RE GIVEN.
YOUR CAR TIRE HAS 14 INCH RIMS
WITH A TIRE THICKNESS OF 4 INCHES.
SO IF THE RIM IS 14 INCHES
THAT WOULD BE THE DIAMETER OF THIS RED CIRCLE
AND THE TIRE THICKNESS IS 4 INCHES,
SO THE DISTANCE FROM HERE TO HERE WOULD BE 4 INCHES.
SO THE RADIUS THAT WE'RE CONCERNED ABOUT
IN THIS PROBLEM
WOULD BE FROM THE CENTER TO THE EDGE OF THE TIRE.
IF THE DIAMETER IS 14,
THEN THE RADIUS OF THE RED CIRCLE IS 7
AND 7 + 4 WOULD GIVE US A RADIUS OF 11 INCHES.
NOW, IT SAYS IF YOU DRIVE 45 MILES PER HOUR
HOW FAST IS THE TIRE SPINNING IN REVOLUTIONS PER SECOND?
SO RIGHT AWAY WE'RE GOING TO HAVE TO CONVERT HOURS
INTO SECONDS.
AND WE'LL ALSO HAVE TO CONVERT MILES INTO INCHES,
BECAUSE OUR RADIUS IS IN INCHES.
SO WHAT WE'RE GOING TO DO
IS DETERMINE HOW MANY INCHES PER SECOND YOU'RE TRAVELING
WHEN YOU'RE TRAVELING 45 MILES PER HOUR.
AND THEN WE'LL DIVIDE THAT BY THE DISTANCE TRAVELED
BY ONE REVOLUTION OF THIS TIRE.
AND ONE REVOLUTION WOULD ACTUALLY BE THE CIRCUMFERENCE
OF THIS OUTER CIRCLE.
SO LET'S GO AHEAD AND SET THIS UP.
LET'S FIRST CONVERT 45 MILES PER HOUR
INTO INCHES PER SECOND,
SO 45 MILES PER 1 HOUR.
WE'RE GOING TO MULTIPLY THIS BY SEVERAL UNIT FRACTIONS
TO DO THE CONVERSIONS.
LET'S FIRST CONVERT MILES INTO INCHES.
AND SINCE WE WANT MILES TO SIMPLIFY OUT
WE'RE GOING TO PUT 1 MILES IN THE DENOMINATOR
AND 5,280 FEET IN THE NUMERATOR.
NOTICE HOW THE UNITS OF MILES WILL SIMPLIFY OUT.
SO NOW I'VE CONVERTED MILES TO FEET
AND NOW WE NEED TO CONVERT FEET INTO MILES.
SO WE'LL PUT 1 FOOT IN THE DENOMINATOR
AND 12 INCHES IN THE NUMERATOR
AND NOW THE UNITS OF FEET HAVE SIMPLIFIED OUT.
BUT WE NOW WE STILL HAVE HOURS AND WE NEED SECONDS.
SO WE NEED SOME MORE UNIT FRACTIONS.
WE WANT TO CONVERT HOURS INTO MINUTES FIRST,
SO WE'LL PUT 1 HOURS IN THE NUMERATOR
AND 60 MINUTES IN THE DENOMINATOR.
AND, AGAIN, THE REASON WE'RE PUTTING HOURS IN THE NUMERATOR
IS SO THAT IT SIMPLIFIES WITH THE HOUR
HERE IN THE DENOMINATOR.
AND NOW WE NEED ONE MORE UNIT FRACTION.
WE NEED TO CONVERT MINUTES INTO SECONDS
AND 1 MINUTE IS EQUAL TO 60 SECONDS.
SO WHAT WE'VE DONE NOW IS CONVERTED 45 MILES PER HOUR
INTO INCHES PER SECOND.
SO NOW WE'LL TAKE ALL OF THIS
AND DIVIDE BY THE DISTANCE TRAVELED
BY ONE REVOLUTION OF OUR TIRE,
WHICH IS THE CIRCUMFERENCE OF THE TIRE.
SO WE'LL DIVIDE ALL THIS BY 2 x PI x 11 INCHES,
AND THIS WILL GIVE US THE REVOLUTIONS PER SECOND.
LET'S GO AHEAD AND USE OUR CALCULATOR FOR THIS.
SO WE'LL MULTIPLY ALL THESE FRACTIONS TOGETHER
AND THEN DIVIDE BY 2PI x 11.
SO WE'LL GO AHEAD AND MULTIPLY ACROSS THE NUMERATOR.
THAT'LL BE 45 x 5280 x 12
AND WE'LL DIVIDE ALL THIS BY 60 x 60.
SO THIS TELLS US WHEN YOU'RE TRAVELING 45 MILES PER HOUR
YOU'RE ALSO TRAVELING 792 INCHES PER SECOND.
AND NOW WE'LL DIVIDE THIS BY 2 x PI x 11
AND THIS WILL GIVE US THE NUMBER OF REVOLUTIONS
PER SECOND.
SO IT'S ROUGHLY 11.46 REVOLUTIONS PER SECOND
WHEN TRAVELING 45 MILES PER HOUR.