The tires on a new compact car have a diameter of 2.0 ft and are warranted for 6

Question

The tires on a new compact car have a diameter of 2.0 ft and are warranted for 60,000 miles. (a) Determine the angle (in radians) through which one of these tires will rotate during the warranty period. (b) How many revolutions of the tire are equivalent to your answer in (a)?

Explanation / Answer

(a) s = r? where: s = arc distance traveled (60,000 miles) r = radius of the tire (1.0 ft) ? = The angle (in radians) through which one of the tires will rotate Since s is in units of miles and r is in units of feet, convert one of these measurements so that both s and r have the same units. I converted s to feet: s = 60,000 miles * (5280 ft/1 mile) = 316,800,000 feet r = 1.0 feet ==> ? = s/r = 316,800,000 feet/1.0 feet = 3.168 x 10^8 radians (b) There is 1 revolution for every 2*pi radian: 1 revolution / (2*pi) rad 3.168 x 10^8 rad * (1 revolution / (2*pi) rad) = 50420285.97 revolutions ==> 5.04 x 10^7 revolutions

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