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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 part (a)

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A) Equation relating arc length to subtended angle:

s = rθ

s = arc length, r = radius, θ = angle

Given values:

s = 6×10⁴mi = 3.168×10⁸ft, r = (2.0ft)/2 = 1.0ft

Plug in and solve for θ:

3.168×10⁸ = 1.0θ

θ = 3.168×10⁸rad

B) One revolution is equal to 2π radians, so divide θ by 2π to obtain the number of revolutions:

3.168×10⁸/(2π)

= 5.042×10⁷ revolutions

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