Physics

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How long would it take for the Earth to complete a full turn if a person at 49.2° northern geographical latitude floats apparently weightlessly across the room? Use REarth = 6,385 km for the radius of Earth

  • Physics -

    How long would it take for the Earth to complete a full turn if a person at 49.2° northern geographical latitude floats apparently weightlessly across the room? Use REarth = 6,385 km for the radius of Earth.

  • Physics -

    Not sure if I understood your question.
    I interpret it as saying "if the Earth is rotating at a yet unknown angular velocity ω such that a person would float weightlessly at latitude 49.2°N, find &omega."

    It is not as simple as it sounds, because the acceleration due to gravity acts towards the centre of the Earth. On the other hand, the rotation of the Earth is around a N-S axis, causing the centripetal force to be at an angle θ with the vertical, where θ is the latitude.

    Assuming that the vertical (towards the centre of the earth) components balance, and the person floating is restrained from flying south by a horizontal rope, then we can do the following calculations:
    Acceleration due to gravity, g = 9.8 m/s²
    Radius of the Earth, R = 6385 km = 6385000 m
    Latitude = 49.2°

    We will find r, the distance of the surface of the earth to the axis of rotation, i.e. measured along the equatorial plane.
    r = Rcos(θ)

    Centripetal acceleration, a
    = rω² (perpendicular to axis of rotation)

    Vertical component of centripetal acceleration, av
    = a cos(θ)
    = rω² cos(&theta)
    = Rω&up2; cos2(&theta)

    Equate av and g, solve for &omega.

    I get 0.0019 radians/sec. which translats to a full rotation in 55 minutes and 14 seconds.

  • Physics-corr -

    Editorial correction:
    Vertical component of centripetal acceleration, av
    = a cos(θ)
    = rω² cos(θ)
    = R ω² cos²(θ)

  • Physics-supp. reading -

    Here's an article complete with figures for supplementary reading:
    http://galitzin.mines.edu/INTROGP/notes_template.jsp?url=GRAV%2FNOTES%2Flatitude.html&page=Gravity%3A%20Notes%3A%20Latitude%20Variations

  • Physics -

    how did you translate 0.0019 radians/sec into minutes?

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