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

Click For Summary

Homework Help Overview

The problem involves determining the rotational speed in revolutions per minute (RPM) at which the tip of a windmill blade will break the sound barrier. The windmill's height and blade length are specified, along with the speed of sound.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the relationship between angular speed in radians per second and the required RPM, questioning the units and conversion needed to reach the final answer.

Discussion Status

Some participants have provided hints regarding the conversion from radians per second to RPM, while others express confusion about the linear speed and its application in the problem. There is acknowledgment of a solution being close at hand, but no explicit consensus on the final steps has been reached.

Contextual Notes

Participants note the need for clarity on units and conversions, as well as the importance of correctly interpreting the original problem statement regarding RPM.

natux
Messages
3
Reaction score
0

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
 
Physics news on Phys.org
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...
 

Similar threads

How Does Wind Turbine Blade Length Affect Power Output?
  • · Replies 2 ·
Replies
2
Views
2K
Mini-Golf Windmill: Find Minimum Linear Speed
  • · Replies 5 ·
Replies
5
Views
3K
Mini Golf Windmill: Find Minimum Linear Speed of Ball
  • · Replies 2 ·
Replies
2
Views
3K
Calculate the height from the speed of sound
  • · Replies 2 ·
Replies
2
Views
8K
Rotational Inertia and Motion problems
  • · Replies 3 ·
Replies
3
Views
2K
Rotational Motion and Gravity/Planetary Orbits review
  • · Replies 9 ·
Replies
9
Views
5K
Undergrad What is the top speed of a fencing weapon?
  • · Replies 36 ·
2
Replies
36
Views
28K
High School Space Ship One (SS1): Breaking the Sound Barrier and Making History
  • · Replies 2 ·
Replies
2
Views
4K
What Are the Key Concepts of Motion and Forces?
  • · Replies 15 ·
Replies
15
Views
7K
Graduate How Does Changing Inertia Affect the Dynamics of a Three-Flywheel System?
  • · Replies 18 ·
Replies
18
Views
5K