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Centripetal Acceleration When Not at the Equator

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    If an object was at P then centripetal force at that point would be :

    Cf = mw2Rcos(phi)

    However, the Gravitational force is

    GMm/R2 Where R is the radius of the planet.

    Is this correct ?
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    I would just like to add one more question.

    If my above formula is true then the centripetal force at the poles is zero.

    Since acceleration due to gravity is Gravitational force - Centripetal force can we say that acceleration due to free fall is larger at the poles then at the equator ?
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    bump
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    I know nothing about physics but surely the equator is just an arbitrary line devised by humans? Why would Centripetal force disappear at the poles? that would result in planes flying into orbit when the go over the Arctic?

    As i said. i know nothing about physics.
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    (Original post by OSharp)
    I know nothing about physics but surely the equator is just an arbitrary line devised by humans? Why would Centripetal force disappear at the poles? that would result in planes flying into orbit when the go over the Arctic?

    As i said. i know nothing about physics.
    Think of a circle.... As the circe becomes a smaller the radius becomes smaller, correct ?

    The centripetal force is dependent on the radius of this circle.

    If you imagine the earth as billions and billions of thin horizontal cricular wedges all stuck together you can see that the 'circle' at the extreme top and bottom (poles) have near zero radius.
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    (Original post by OSharp)
    I know nothing about physics but surely the equator is just an arbitrary line devised by humans? Why would Centripetal force disappear at the poles? that would result in planes flying into orbit when the go over the Arctic?

    As i said. i know nothing about physics.
    There's nothing imaginary about the equator.

    Assume for simplicity that the Earth is a sphere, spinning on its axis. If you stand on the equator, you are rotating in a circle, with a radius equal to the radius of the Earth. If you stand on one of the poles, you are not rotating in a circle at all. Anywhere in between, and you are rotating in a circle with a radius less than the radius of the Earth.

    Each of these situations will affect the centripetal force you feel.

    However, wherever you are, you still feel the same gravitational attraction because of your mass and the mass of the Earth.

    Original working out in the first post looks OK to me.
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    Could you confirm my question in the second post. Thanks for looking into it for me !

    (Original post by Pangol)
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    yes, assuming the sphere is rotating about the Y axis

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