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Earth Rotation

  1. Aug 31, 2004 #1
    Assume the earth is spherical. Relative to someone on the rotation axis, what is the linear speed of an object on the surface if the radius vector from the center of the earth to the object makes an angle of 62.0 degrees with the axis of rotation. Radius of the earth = 6.37·103 km

    I know that the earth is rotating, 7.29E-05 in radians/second.

    Also, I think the formula to find linear speed for motion in a circle is the radius times the angular velocity. I get an angular velocity of 850480.10973937 r/s and I do not think this is right?
     
  2. jcsd
  3. Aug 31, 2004 #2
    I'm not sure how you arrived at your answer, but the question is asking for the linear speed (not the angular velocity of object). The angular velocity of any object on the earth is actually the same. To see this, note that the path each [stationary] object traces out in space is a circle; and, moreover, each object traces its circle in the same amount of time (namely 24 hours).

    The linear speed of a body is equal to the product of the angular speed and radius of the circle it is tracing out. For the body related to the problem, the angular speed is known and the radius can be determined as r = R sin th. Now you can just plug in.
     
    Last edited by a moderator: Aug 31, 2004
  4. Aug 31, 2004 #3

    Doc Al

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    Staff: Mentor

    OK, that's 6.37E+3 km.
    OK, that's the angular velocity.
    Right. Find the radius of the circle traced out by that object.
    Well... the angular velocity you already found. (That's the rotation of the earth which you gave above.) Now find the linear speed (in m/s or km/s), using the idea you just supplied yourself. (I have no idea where the number you calculated came from. If you're still stuck, describe exactly how you calculated it.)
     
  5. Aug 31, 2004 #4
    So I multiply 7.29E-05 by sin 62 then multiply that by 6370km.

    and I get 0.41 km/s or 4.10E+02 m/s

    since I have this info do I find the objects acceleration by a= v2/r. r=6.37E+3 km
     
    Last edited: Aug 31, 2004
  6. Aug 31, 2004 #5
    that does give the correct answer, but the reasoning is a little off. your multiplying the radius of the earth by the sin 62 first in order to find the radius of the circle the object traces out. it would help to draw a picture to see this. you could take the origin to be the center of the earth, the y-axis to point to the north pole, and let the x-axis point toward the position on the equator that "lines up" with the object.
     
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