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

[natux]

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

 

[SteamKing]

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'.

 

[natux]

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.

 

[sun18]

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.

 

[Redbelly98]

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.

 

[natux]

Thanks, I got it figured out, I don't know why this confused me so much...