Question 914718
Throughout this problem, I will use the constant pi. That is approximately equal to 3.14; however, you can use a more accurate approximation (say pi = 3.1416) to get a more accurate answer.


Also, even if you ignore pi and its approximations, there will be rounding errors that accumulate. So keep this in mind.


A)


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.

-------------------------------------------------------


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)



-------------------------------------------------------



(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 <font color="red">336.306038495031 revolutions per minute</font> (this is approximate).


=============================================================================

B)


Take the answer from part A) and multiply it by the conversion factor (2 pi radians/1 rev) to convert to "radians per minute"


This works because 2pi radians = 1 revolution


(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 <font color="red">2,112.0019217488 radians per minute</font>



Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at <a href="mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help">jim_thompson5910@hotmail.com</a>
or you can visit my website here: <a href="http://www.freewebs.com/jimthompson5910/home.html">http://www.freewebs.com/jimthompson5910/home.html</a>


Thanks,


Jim