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Uniform circular motion, earth's rotation

  1. Aug 21, 2011 #1
    The earth rotates once per day about an axis passing through the north and south poles, an axis that is perpendicular to the plane of the equator. Assuming the earth is a sphere with a radius of 6.38 x 106 m, determine the speed and centripetal acceleration of a person situated at a latitude of 30.0 degrees north of the equator.

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    My Attempt
    I understand that we are looking at a cross section of the earth at latitude 30.0 degrees north of the equator. I also understand how to get to the answer:

    Given
    T = 1 day = 86, 400 seconds

    1. Find velocity from V = (2pi*r)/T

    2. Take the velocity from the previous equation and plug into to find ac:
    ac = v2/r

    I know that the radius at 30 degrees north of the equation is rearthcos30....My question is: WHY is the radius rearthcos30? I cannot see the geometry behind this conclusion!!! :(
     
    Last edited: Aug 21, 2011
  2. jcsd
  3. Aug 21, 2011 #2

    gneill

    User Avatar

    Staff: Mentor

    The radius of import is the distance to the axis of rotation. For a latitude 30.0° N, how would you calculate that distance?
     
  4. Aug 21, 2011 #3
    Wow - this was a very silly question to ask on my part. When I saw the answer, it literally slapped me in the face. I can't believe I didn't see that...Thank you gneill.
     
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