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Homework Help: Centrifuge question

  1. Oct 28, 2004 #1
    ok, you are using a centrifuge. the centripetal acceleration of the sample is 5.05E3 times larger than the accelleration due to gravity. how many revolutions/minute is the sample making if it is located at a radius of 4.62 cm from the axis of rotation?

    i think i use: centripetal accellearion = (v^2)/r
    so... 5.05E6*9.8m/s = v^2 / 4.62cm
    v = 47.8167 rev/min. but i get it incorrect.. any hints?
     
  2. jcsd
  3. Oct 28, 2004 #2

    Galileo

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    Why take [itex]5.05^6[/itex] times g, instead of the given [itex]5.05^3[/itex]?

    Edit: Nevermind, that was a typo, you used the correct value.

    But v is the velocity, not the number of revolutions per minute.
    The time it takes (in seconds) for one revolution is [tex]T=\frac{2\pi r}{v}[/tex]
     
    Last edited: Oct 28, 2004
  4. Oct 28, 2004 #3
    oops sorry. i meant 5.05^3 in my calculations. i used it, but just typed it here wrong.
     
  5. Oct 28, 2004 #4
    ok, in my first equation. when i have the radius, should that be 4.62cm or .0462m ? because i used .0462m even though i wrote 4.62cm
     
    Last edited: Oct 28, 2004
  6. Oct 28, 2004 #5
    You want angular velocity, you're using the linear velocity formula!
    Just use simple substitution...
    r = Radius
    Because v = rw (Where w is angular velocity)
    Centripetal Acceleration = (rw)^2/r Which gives:
    (r^2w^2)/r = rw^2
    And Radius should ALWAYS be in metres, unless asked otherwise..
    Just solve for w.
     
    Last edited: Oct 28, 2004
  7. Oct 28, 2004 #6
    so everything i did was wrong? ok.
    ok so i took:
    5.05E3*9.8 = .0462w^2
    w=1034.993778 and is that revolution/sec?
    is that better?
     
  8. Oct 28, 2004 #7
  9. Oct 29, 2004 #8

    Galileo

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    That would radians per second. You traverse [itex]2\pi[/itex] radians in one revolution, so dividing [itex]\omega[itex] by [itex]2\pi[/itex] will give the number of revolutions per second.

    And no, it's not true that everything you did was wrong. You could take
    [tex]f=\frac{1}{T}=\frac{v}{2\pi r}[/tex] which also gives the number of revolutions per second.
     
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