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RPM with given distance

  1. Jul 24, 2009 #1
    A space station is in the shape of a hollow ring, 450 m in diameter. At how many revolutions per minute should it rotate in order to simulate Earth's gravity-that is, so that the normal force on an astronaut at the outer edge would be the astronaut's weight on Earth?

    All I got so far was finding the circumference=pid=1413 meters. I'm stuck, I don't know what to do next. Help please!
     
  2. jcsd
  3. Jul 24, 2009 #2

    rock.freak667

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    So the space station is rotating, thus there is a centripetal force. Do you know what that is?
     
  4. Jul 24, 2009 #3
    Yeah, it's the force that is the same direction as acceleration, towards the center.
     
  5. Jul 24, 2009 #4

    rock.freak667

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    Right then. So you want the space station to produce a force which is equal to the weight of the astronaut. Can you make a relation between this force and the weight?
     
  6. Jul 24, 2009 #5
    would it just be N=mg?
     
  7. Jul 24, 2009 #6

    rock.freak667

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    Yes the normal force on the astronaut is =mg. BUT you want the space station to spin to produce a force which equals mg. Do you know any formulas for centripetal force?
     
  8. Jul 24, 2009 #7
    F=mrw^2?
     
  9. Jul 24, 2009 #8

    rock.freak667

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    yes, so you want mw2r=mg

    can you find w and then convert that to RPM?
     
  10. Jul 24, 2009 #9
    okay i got w=.20 but I don't know how to convert that to RPM. Wouldn't the units on w by 1/s^2? Is there a formula or conversion factor to get it to RPM?
     
  11. Jul 24, 2009 #10

    Astronuc

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    Note that in the equation mw2r=mg, the mass is the same.

    So dividing by mass, it become w2r=g.

    g had unit of m/s2, and since r had units of m (meters, length), then w2 must give units of 1/s2.

    w is angular frequency which is expressed in 1/s, and it's actually radians/s. Now since 1 revolution passes through 2pi radians, then 1 rps (revolution per second) = 2pi rad/s.

    The frequency in revolutions per unit time = f = w/2pi = 1/T, where T = the period.

    Conversely, w = 2pi f
     
  12. Jul 24, 2009 #11

    rock.freak667

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    Right then w=0.2 rad/s and you want it in revolutions per minute.

    In 1 revolution, the station rotates 2pi radians.
    So 1 rad = 1 rev/2pi.

    60 seconds = 1min

    so

    [tex]1 \frac{radian}{seconds} = \frac{60}{2 \pi} revolutions/min[/tex]
     
  13. Jul 24, 2009 #12
    Okay, I got it now. Thank you!!
     
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