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Space station problem

  1. Nov 17, 2008 #1
    1. The problem statement, all variables and given/known data
    A space station consists of two doughnut shaped living chambers, A and B, that have the radii shown in the drawing. As the station rotates, an astronaut in chamber A is moved 2.40 x 102 m along a circular arc. How far along a circular arc is an astronaut in chamber B moved during the same time?

    here is the picture for more reference:

    2. Relevant equations
    i dont know if these will help we just got alot today so here:
    w=[tex]\theta[/tex]/Delta t
    *v=vo+at ~ w=wo+[tex]\omega[/tex]t
    *v2=vo2+2ax ~ w2=wo2+2[tex]\omega[/tex][tex]\theta[/tex]
    *x=vot+(1/2)at2 ~ [tex]\theta[/tex]=wot+(1/2)at2

    the ones with * means i changed it to what the problem is about. means the same thing just different letters so you wont get confused i guess.

    3. The attempt at a solution
    i have no idea what im supposed to do. i know the arc length should be the same as the radius because its has something to do with radians? i have no clue what im supposed to do. please help me.

    thank you!
  2. jcsd
  3. Nov 17, 2008 #2


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    Hi sweedeljoseph! :smile:

    Arc-length = radius times angle (with angle measured in radians):

    arc-length = rθ :wink:

    (so the arc-length equals the radius only if the arc-angle is 1 radian!)
  4. Nov 17, 2008 #3
    how would i know if the angle is 1 radian?
  5. Nov 17, 2008 #4


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    2π radians is 360º

    so 1 radian = (180/π)º. :smile:
  6. Nov 17, 2008 #5
    i know that but how do you know from the problem what the angles are?
  7. Nov 18, 2008 #6


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    Hi sweedeljoseph! :smile:

    This is a very simple symmetry problem (expansional symmetry :wink:) …

    you don't need to know anything about angles or radians

    the space station is rigid, so if A goes 240m round a circle of radius 320m, then B goes … round a circle of radius 1100m? :smile:
  8. Nov 18, 2008 #7
    my teacher showed me how to do this today. i feel so stupid. haha.

    thank you though!
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