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
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...
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

How Does Wind Turbine Blade Length Affect Power Output?
Replies
2
Views
2K
Mini-Golf Windmill: Find Minimum Linear Speed
Replies
5
Views
3K
Mini Golf Windmill: Find Minimum Linear Speed of Ball
Replies
2
Views
3K
Calculate the height from the speed of sound
Replies
2
Views
8K
Rotational Inertia and Motion problems
Replies
3
Views
2K
Rotational Motion and Gravity/Planetary Orbits review
Replies
9
Views
5K
What is the top speed of a fencing weapon?
Replies
36
Views
27K
Space Ship One (SS1): Breaking the Sound Barrier and Making History
Replies
2
Views
4K
What Are the Key Concepts of Motion and Forces?
Replies
15
Views
6K
How Does Changing Inertia Affect the Dynamics of a Three-Flywheel System?
Replies
18
Views
5K

Hot Threads

Recent Insights

Back
Top