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

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SUMMARY

The discussion centers on calculating the RPM at which the tip of a windmill blade will break the sound barrier, defined as 1125 ft/sec. The windmill has a height of 400 feet and each blade measures 130 feet in length. The linear speed is derived using the formula v = rω, leading to an angular speed of approximately 9 radians per second. The conversion from radians per second to RPM is necessary to provide the final answer in the requested units.

PREREQUISITES
  • Understanding of angular speed and linear speed concepts
  • Familiarity with the relationship between radians and revolutions
  • Knowledge of basic physics equations related to rotational motion
  • Ability to perform unit conversions, specifically from radians per second to RPM
NEXT STEPS
  • Learn about the conversion from radians per second to RPM
  • Explore the physics of rotational motion and its applications
  • Study the impact of blade length on windmill efficiency
  • Investigate sound barrier concepts in relation to different materials and structures
USEFUL FOR

Students studying physics, engineers involved in wind turbine design, and anyone interested in the dynamics of rotational motion and sound barriers.

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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