Question

A new midsize car has tires with a diameter of 26.5 inches. The tires have a tread-life warranty of 61,000 miles.

A new midsize car has tires with a diameter of 26.5 inches. The tires have a tread-life warranty of 61,000 miles. (a) How many radians will the tires rotate through within the full warranty length? rad (b) How many revolutions is this equivalent to? rev

Answer 1

Sol::

Given

Diameter (D) = 26.5
tread-life warranty = 61,000 miles

(a)

linear distance
s = 61,000 miles
= 61000*5280 ft
= 322,080,000 ft
Radius of tire r = 26.5/ 2
= 13.25 inch
= 1.1041 ft

angle θ = s / r
= 322,080,000/1.1041
= 291,712,707.182 rad
≈ 2.92*10^8 rad

(b)

so no. of revs = θ/ 2π
= 2.92*10^8/2π revs
= 4.65*10^7 revs

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