Question

A car is moving at a rate of 28 miles per hour and the diameter of its wheels is about 2 1/3 feet. Find the angular speed of the wheel in radians per minute.

Answer 1

The diameter of the wheel is 2 1/3 ft. So d = 2 + 1/3
Circumference
C = pi*d
C = 3.14*(2 + 1/3)
C = 7.326667

The circumference is roughly 7.32666 feet.
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Convert 7.32666 feet to miles

(7.32666 feet)*(1 mile/5280 feet) = 7.32666/5280 = 0.001387625 miles

7.32666 feet = 0.001387625 miles (approximate)


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(28 miles/1 hour)*(1 revolution/0.001387625 miles) = 28/0.001387625 = 20,178.3623097019 revolutions per hour


Now convert from "revolutions per hour" to "revolutions per minute"


(20,178.3623097019 rev/1 hour)*(1 hour/60 minutes) = 20,178.3623097019/60 = 336.306038495031


The final answer for part A) is 336.306038495031 revolutions per minute (this is approximate).

336.306038495031 rev/1 minute)*(2pi radians/1 rev) = 336.306038495031*2pi = 336.306038495031*2*3.14 = 2,112.0019217488

So the angular speed is roughly 2,112.0019217488 radians per minute