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What is the angular speed in revolution per minute?

  1. Nov 26, 2013 #1
    1. The problem statement, all variables and given/known data
    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)?



    2. Relevant equations

    a(centripedal)= v^2/radius
    v=ωr

    3. 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?
     
  2. jcsd
  3. Nov 26, 2013 #2
    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.
     
  4. Nov 26, 2013 #3
    It's correct up to the very last step. Then, you got the decimal point in the wrong place.

    Chet
     
  5. Nov 26, 2013 #4
    yeah I realize that. it seems that I have to convert rad/s to rpm
     
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