The number of revolutions per minute the wheels are turning is 570.53 rpm.
The correct answer is E
The given parameters:
linear speed of the car, v = 55 miles per hour
diameter of the car's wheel, d = 2.7 ft
radius of the car's wheel, r = 1.35 ft
To find:
Convert the given speed in miles per hour to feet per minutes
1 mile = 5280 ft
[tex]v = 55\ \frac{miles}{hour} \times \frac{5280 \ ft}{1 \ mile} \ \times \ \frac{1 \ hour}{ 60 \ \min} = 4,840 \ \frac{ft}{\min}[/tex]
Calculate the angular speed of the car in radian per minute:
[tex]\omega = \frac{v}{r} = \frac{4840 \ ft/min}{1.35 \ ft} = 3585.185 \ \frac{rad}{\min}[/tex]
Calculate the angular speed of the car in revolution per minute:
[tex]\omega = \frac{3585.185 \ rad}{\min} \times \frac{1 \ rev}{2\pi} = 570.53 \ \frac{rev}{\min}[/tex]
Thus, the number of revolutions per minute the wheels are turning is 570.53 rpm.
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