calculate circumference of tire = C=2*pi*r = 2*3.14812 = 75.36
5280 ft in a mile
calculate feet per hour = 5280/34 = 179,520 ft/hr
find inches per hour 179520*12 = 2154240
calculate inches / minute = 2154240/60 = 35904 inches per minute
divide that by tire circumference
35904/75.36 = 476.43 revolutions per minute
The tires of car is turning at the rate of 476.70 revolutions per minute (rpm).
Given data:
The speed of car is, [tex]v = 34 \;\rm mi/h = 34 \times 5280 =179520 \;\rm ft/h[/tex].
The diameter of the tire is, [tex]d = 24 \;\rm in = 24 \times 0.083=1.992 \;\rm ft[/tex].
The given problem is based on the angular speed and number of revolutions made by the tires. The expression for the angular speed is,
[tex]\omega = \dfrac{v}{r}[/tex]
Here, r is the radius of tire and v is the linear speed of car. So, radius is, r = d/2.
Solving as,
[tex]\omega = \dfrac{179520}{1.992/2}\\\\\\\omega = \dfrac{179520}{0.996}\\\\\\\omega =180240.96\;\rm rad/h[/tex]
Now convert the given value to rad/s as,
[tex]\omega =180240.96 \times 0.000277 \;\rm rad/s =49.92 \;\rm rad/s[/tex]
Now, finally convert the above value to rotation per minute (rpm) as,
[tex]\omega =\dfrac{2 \pi \times n}{60} \\\\49.92 =\dfrac{2 \pi \times n}{60}\\\\n= 476.70 \;\rm rpm[/tex]
Thus, we can conclude that the tires of car is turning at the rate of 476.70 revolutions per minute (rpm).
learn more about the angular speed here:
https://brainly.com/question/19557693
