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Acceleration associated with the Earth’s spin

  1. May 17, 2017 #1
    1. The problem statement, all variables and given/known data

    Calculate the acceleration associated with
    the Earth’s rotation about its axis (assume an equatorial point).
    2. Relevant equations

    About center of mass motion
    Γ=Iα

    3. The attempt at a solution
    Since the external forces acting on the earth are gravitational forces and hence there is no torque acting on the earth.
    Hence the acceleration associated with
    the Earth’s rotation about its axis (assume an equatorial point) is zero.
     
  2. jcsd
  3. May 17, 2017 #2

    Drakkith

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    Staff: Mentor

    You've found the angular acceleration, but I believe the question is asking for the acceleration of a point of the Earth's surface on the equator due to Earth's spin. In other words, if you were standing at the equator, what would the component of your acceleration associated with the Earth's rotation be?
     
  4. May 17, 2017 #3
    o.k. I got it.
    Thank you.
     
  5. May 17, 2017 #4
    Then, the acceleration would be Rω2 towards the center where ω is the angular speed of the earth rotation and R is the distance between the center of the earth and its equator,wouldn't it?
     
  6. May 17, 2017 #5

    Drakkith

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    Staff: Mentor

    That looks about right. And what direction is the acceleration in?
     
  7. May 17, 2017 #6
    The acceleration is towards the center of the earth, radially inward.
     
  8. May 17, 2017 #7

    Drakkith

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    Staff: Mentor

    Is it? Remember we're talking about the acceleration associated with the Earth's spin, not its gravity.
     
  9. May 18, 2017 #8
    Let's model the earth as a spinning ball for this problem.
    I am sitting on the equator.
    Now from an inertial frame,I will be in a uniform circular motion with angular speed ω and radius R.
    according to newton's 2nd Law of motion,
    F = ma = 2 R(-## \hat r ##)
    So ,the direction is radially inward.
     
  10. May 18, 2017 #9

    Drakkith

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    Staff: Mentor

    I apologize, I was mistaken. Of course the direction is radially inward. Otherwise the point wouldn't be kept in circular motion. It's been awhile since I took my last physics class. :rolleyes:
     
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