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Angular Acceleration of a centrifuge

  1. Feb 17, 2009 #1
    A centrifuge in a medical laboratory rotates at an angular speed of 3400 rev/min. When switched off, it rotates 48.0 times before coming to rest. Find the constant angular acceleration of the centrifuge.

    Relevent equations: ωf = ωi + αt

    My work:
    I found out the time by (48 rev)(1min/3400 rev)(60 sec/min) = 0.847 seconds

    I then converted the rev/min to rad/sec (3400 rev/min)(2pi/1rev)(1min/60sec)= 356 rad/sec

    So I set the problem up like 0=356 rad/sec + α(0.847 seconds)
    -356/0.847=α
    α = -420 rad/s^2
     
  2. jcsd
  3. Feb 17, 2009 #2

    LowlyPion

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    Last edited: Feb 17, 2009
  4. Feb 17, 2009 #3
    yes but couldn't you find time using the equation i did earlier? i'm trying to solve for a tho....

    However, if I were to calculate what you put in...

    0=3400 rev/min+2a(48rev)
    -3400/96=a
    a=-35 min^-1
     
    Last edited: Feb 17, 2009
  5. Feb 17, 2009 #4

    LowlyPion

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    Yes. You can use that equation for time, once you've found the α based on the θ given and the initial ω.
     
  6. Feb 17, 2009 #5
    i edited my last post, is that correctly calculated?
     
  7. Feb 17, 2009 #6

    LowlyPion

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    Well I left an exponent out of my earlier post and I corrected that apparently after you used it.

    Instead of blindly using formulas, I encourage you to review the link and think about how the rotational kinematic equations relate to the regular one dimensional kinematics that I think you already know.

    But that aside (and the exponent of the initial ω corrected) your calculation hasn't accounted for the conversion from min to sec. (Unless you don't need your answer in sec.)
     
  8. Feb 17, 2009 #7
    if i put it in seconds it ends up being 0.583 s^-1 but that' can't be the acceleration....shouldn't it be to the -2?
     
  9. Feb 17, 2009 #8

    LowlyPion

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    Look you need to understand the equations.

    ωf2 = ωi2 + 2*α*θ

    But they give you revolutions. And there are 2π radians in a revolution and θ is in radians.
     
  10. Feb 17, 2009 #9
    ohhhh i see now, thanks lowly ^^
     
  11. Feb 17, 2009 #10

    LowlyPion

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    Remember the acceleration α they want is (-) because you are slowing down to a stop.
     
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