Centripetal Acceleration Problem: Finding Angular Speed

[Nahtee]

Hi all, I've been lurking around the forums for a while to get help with homework but I figured I'd finally make an account to get direct feedback.

I'm having problems with this centripetal acceleration problem,

Homework Statement

"In an old-fashioned amusement park ride, passengers stand inside a 5.4-m-diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about a vertical axis. Then the floor on which the passengers are standing suddenly drops away! If all goes well, the passengers will "stick" to the wall and not slide. Clothing has a static coefficient of friction against steel in the range 0.62 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. A sign next to the entrance says "No children under 30 kg allowed." What is the minimum angular speed, in rpm, for which the ride is safe?"

Homework Equations

F=ma, Ff=µN, ω=v^2/r

The Attempt at a Solution

So, I started out drawing a FBD with Ff up, Fg down, and Fn towards the center of the circle. Applying N2L gave me 0=µN-mg=µω^2r-g, so ω=sqrt(g/rµ). From this equation its clear that the angular velocity would be lowest when µ=1, since its in the denominator. So after I plugged in the values for g and r I got sqrt(9.81/2.7)= 1.906rad/s. Then dividing that by 2pi to go from radians to revolutions gave me 0.3033rps, x60 to convert to minutes = 18.20rpm.
My online homework site marked this as wrong and says the answer is 23rpm, but even after double checking my work and trying to work backwards from the 23rpm I can't figure out where I went wrong. Any thoughts?

 

[PhanthomJay]

What would happen if someone was wearing clothing with the friction coefficient less than 1 and the ride was rotating at 18.2 rpm?

 

[Nahtee]

What would happen if someone was wearing clothing with the friction coefficient less than 1 and the ride was rotating at 18.2 rpm?

Ah I see, using the 0.62 coefficient gives me the correct answer. If someone had clothing with the coeff of friction less than 1 and the ride was rotating at 18.2rpm there wouldn't be enough centripetal acceleration to hold them to the wall, so they would fall off. Thanks for you're help!