At how many rpms will a blade tip break the sound barrier

AI Thread Summary
To determine the RPM at which a windmill blade tip breaks the sound barrier, the speed of sound is 1125 ft/sec. The blade length is 130 feet, leading to the calculation of angular speed in radians per second, which is approximately 9 rad/sec. To convert this angular speed into RPM, a conversion factor is applied, as RPM refers to revolutions per minute. The confusion arose from transitioning between radians per second and RPM, but the linear speed was correctly identified as 1125 ft/sec. Ultimately, the problem was resolved with the correct understanding of the necessary conversions.
natux
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Homework Statement


The windmill is 400 feet tall and each of it's three blades are 130 feet long. At how many rpms will a blade tip break the sound barrier? Speed of sound: 1125ft/sec


Homework Equations


Linear speed: v = rω
Angular speed: ω = Θ/Time


The Attempt at a Solution


1125ft/sec = 130ft(ω)
ω = 1125ft/sec * 1rad/130ft ≈ 9
 
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What are the units of the number 9? Are they RPMs like what was requested in the OP?

Hint: RPM usually means 'revolutions per minute'.
 
Sorry, the 9 is in radians per second, but the problem is I get stuck there. I know I need the linear speed...but I don't how to go about doing that in this situation.
 
You have already solved this problem! You are looking for an answer in rpm's. You have a solution in radians per second. There is only a conversion to do from here.
 
natux said:
I know I need the linear speed...but I don't how to go about doing that in this situation.
You already have the linear speed, 1125 ft/sec, as used in your originally posted attempt at a solution.
 
Thanks, I got it figured out, I don't know why this confused me so much...
 

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