Earth as a perfect sphere and an object trying to stand still

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I have imagined the Earth as a perfect sphere with uniform mass density and I put an object somewhere between the equator and the north pole at rest with respect to earth. And also in my imaginery world, there is no air resistance.



When I draw the free body diagram of the object including the pseudo force, I cannot see how these three forces will cancel.



Would we need force of friction in order to be able to stand still in my imaginary world?



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newtonian-mechanics newtonian-gravity free-body-diagram equilibrium centrifugal-force







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  • Related: physics.stackexchange.com/q/8074/2451 , physics.stackexchange.com/q/69562/2451 , physics.stackexchange.com/q/9751/2451 and links therein.
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I have imagined the Earth as a perfect sphere with uniform mass density and I put an object somewhere between the equator and the north pole at rest with respect to earth. And also in my imaginery world, there is no air resistance.



When I draw the free body diagram of the object including the pseudo force, I cannot see how these three forces will cancel.



Would we need force of friction in order to be able to stand still in my imaginary world?



enter image description here






newtonian-mechanics newtonian-gravity free-body-diagram equilibrium centrifugal-force







share|cite|improve this question























  • Related: physics.stackexchange.com/q/8074/2451 , physics.stackexchange.com/q/69562/2451 , physics.stackexchange.com/q/9751/2451 and links therein.
    – Qmechanic♦
    2 hours ago













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I have imagined the Earth as a perfect sphere with uniform mass density and I put an object somewhere between the equator and the north pole at rest with respect to earth. And also in my imaginery world, there is no air resistance.



When I draw the free body diagram of the object including the pseudo force, I cannot see how these three forces will cancel.



Would we need force of friction in order to be able to stand still in my imaginary world?



enter image description here






newtonian-mechanics newtonian-gravity free-body-diagram equilibrium centrifugal-force







share|cite|improve this question















I have imagined the Earth as a perfect sphere with uniform mass density and I put an object somewhere between the equator and the north pole at rest with respect to earth. And also in my imaginery world, there is no air resistance.



When I draw the free body diagram of the object including the pseudo force, I cannot see how these three forces will cancel.



Would we need force of friction in order to be able to stand still in my imaginary world?



enter image description here






newtonian-mechanics newtonian-gravity free-body-diagram equilibrium centrifugal-force




newtonian-mechanics newtonian-gravity free-body-diagram equilibrium centrifugal-force






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edited 2 hours ago









Qmechanic♦

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physicsguy19

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  • Related: physics.stackexchange.com/q/8074/2451 , physics.stackexchange.com/q/69562/2451 , physics.stackexchange.com/q/9751/2451 and links therein.
    – Qmechanic♦
    2 hours ago

















  • Related: physics.stackexchange.com/q/8074/2451 , physics.stackexchange.com/q/69562/2451 , physics.stackexchange.com/q/9751/2451 and links therein.
    – Qmechanic♦
    2 hours ago
















Related: physics.stackexchange.com/q/8074/2451 , physics.stackexchange.com/q/69562/2451 , physics.stackexchange.com/q/9751/2451 and links therein.
– Qmechanic♦
2 hours ago





Related: physics.stackexchange.com/q/8074/2451 , physics.stackexchange.com/q/69562/2451 , physics.stackexchange.com/q/9751/2451 and links therein.
– Qmechanic♦
2 hours ago











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Indeed, you need friction. Otherwise this object will slide to equator just as you expect.



In fact, all the objects will slide there to form equatorial bulge and eventually the sphere will be turned into new shape with surface orthogonal to $vecg+omega^2 vecr$ at each point. That is exactly what happens to planets in reality while they are still liquid.






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    Indeed, you need friction. Otherwise this object will slide to equator just as you expect.



    In fact, all the objects will slide there to form equatorial bulge and eventually the sphere will be turned into new shape with surface orthogonal to $vecg+omega^2 vecr$ at each point. That is exactly what happens to planets in reality while they are still liquid.






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      up vote
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      Indeed, you need friction. Otherwise this object will slide to equator just as you expect.



      In fact, all the objects will slide there to form equatorial bulge and eventually the sphere will be turned into new shape with surface orthogonal to $vecg+omega^2 vecr$ at each point. That is exactly what happens to planets in reality while they are still liquid.






      share|cite|improve this answer








      New contributor




      FiatLux is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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        up vote
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        up vote
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        Indeed, you need friction. Otherwise this object will slide to equator just as you expect.



        In fact, all the objects will slide there to form equatorial bulge and eventually the sphere will be turned into new shape with surface orthogonal to $vecg+omega^2 vecr$ at each point. That is exactly what happens to planets in reality while they are still liquid.






        share|cite|improve this answer








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        FiatLux is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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        Indeed, you need friction. Otherwise this object will slide to equator just as you expect.



        In fact, all the objects will slide there to form equatorial bulge and eventually the sphere will be turned into new shape with surface orthogonal to $vecg+omega^2 vecr$ at each point. That is exactly what happens to planets in reality while they are still liquid.







        share|cite|improve this answer








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        answered 1 hour ago









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