What is the angular speed in revolution per minute?

[jimmyboykun]

Homework Statement

You are consulting for an amusement park that wants to build a new "Rotor" ride. In order to increase capacity, they would like to build a unit with a 14.2-ft diameter. The Rotor should provide a centripetal acceleration of 3g. What must be the angular speed in revolutions per minute (rpm)?

Homework Equations

a(centripedal)= v^2/radius
v=ωr

The Attempt at a Solution

1ft=0.3048m---> 14.2ft*0.3048m/ft= 4.33m

4.33/2= 2.16(this is the radius)

3(9.81m/s^2)= 29.43m/s^2

v^2=2.16*29.43m/s^2=63.5688

sqrtv=sqrt63.5688=7.97m/s

v=ωr
7.97m/s=ω2.16

7.97/2.16=ω

ω=3.69rad/s

3.69rad/s*1rev/2∏*60s/1m= 344.77rpm

344.77rpm is my final answer but I got that wrong, where did I go wrong in my calculations?

 

[xophergrunge]

It seems like you are taking the correct steps. However, I get a different numerical answer than you do.

Also, may I suggest that you don't plug all of those numbers in immediately, and just work with symbols until you have an expression for what it is you are looking for? It'll make the work easier for you, and you'll be less error prone.

 

[Chestermiller]

It's correct up to the very last step. Then, you got the decimal point in the wrong place.

Chet

 

[jimmyboykun]

yeah I realize that. it seems that I have to convert rad/s to rpm

 

[Nickie]

Your calculations are mostly correct, but you made a small mistake in converting from meters to feet. The radius should be 2.16 feet, not 2.16 meters. This will give you a final answer of approximately 207 rpm.