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.
_________rad

(b) How many revolutions of the tire are equivalent to your answer in (a)?
_________rev

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

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.