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Homework Help: Rotational Kinematics? Revolutions of a propeller?

  1. Jul 8, 2010 #1
    1. The problem statement, all variables and given/known data
    An airplane engine starts from rest; and 2 seconds later, it is rotating with an angular speed of 420 rev/min. If the angular acceleration is constant, how many reovlutions does the propeller undergo during this time?


    2. Relevant equations
    [tex]\theta[/tex] = [tex]\omega[/tex] 0 t +1/2 [tex]\alpha[/tex] t^2

    [tex]\alpha[/tex] = [tex]\Delta[/tex] [tex]\omega[/tex] / [tex]\Delta[/tex]



    3. The attempt at a solution
    I thought that if by converting rev/s to rad/s I could use the angular acceleration to somehow find the number of revolutions made in 2 seconds. But I'm not sure if this requires converting, or even if I am on the right track with the angular acceleration.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 8, 2010 #2

    Ush

    User Avatar

    1. to do your calculations, you do require converting from rev/m to rad/s
    2. what equation relates angular velocity to angular acceleration and time?
     
  4. Jul 8, 2010 #3
    1) So, 420 rev/s would be 840(pi). (I can't find the Pi character) because 1 rev=2(pi) rad. Correct?

    2) The equation should be [tex]\omega[/tex] = [tex]\omega[/tex] 0 + [tex]\alpha[/tex] t
     
  5. Jul 8, 2010 #4

    Ush

    User Avatar

    Your question says 420 rev/m (revolutions per minute), not 420rev/s.
    you first need to convert 420 rev/m to rev/s

    correct,
    you are given enough information to calculate angular acceleration.

    now, you can use your angular displacement equation to calculate the number of radians rotated in 2 seconds.

    you can then convert radians to revolutions.
     
  6. Jul 8, 2010 #5
    OK, so let's see. 420 rev/MIN is 7 rev/s, which is 44 rad/s. Rearranging the kinematic equation to be [tex]\alpha[/tex] = vf /t and substituting, I get the angular acceleration to be 22 rad/s^2. Then, if the initial velocity is 0 rad/s, the final velocity is again 44 rad/s. This converted to rev/s is 44/2(pi), which equals 7 revolutions. I think I took the long way around to get here, but does this seem like the correct process? Or at least it lead to the correct answer?
     
  7. Jul 8, 2010 #6

    Ush

    User Avatar

    after you find your angular acceleration, (22rad/s^2). You need to find your angular displacement. (Remember, angular displacement is the number of radians the propeller turns)

    so no, 7 revolutions is not the correct answer.
     
  8. Jul 8, 2010 #7
    Jeez, this problem has just worked me over, and for no good reason. OK, simply substituting everything into the angular displacement equation, then converting back to revolutions, I get 14 rev. I can't tell you how much I appreciate the help, especially since you took the time to go step by step with me, without just tossing out everything I needed at once.
    My sincerest thanks,
    JHCreighton
     
  9. Jul 8, 2010 #8

    Ush

    User Avatar

    sorry, 7 revolutions was the correct answer. I didn't do the math, I just looked at what you were saying.. But if you do the math
    --
    wf^2 = wi^2 + 2⍺θ
    rearrange for θ

    OR

    θf = θi + Wit + ½⍺t^2
    rearrange for θ
    --

    θ turns out to be 44radians = 7 revolutions =p
     
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