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

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 imaginary 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?

After @Fiatlux's answer, I've realized that I may even have discovered for myself the fundamental reason behind Earth's real shape accidentally.

I have another thing that's bugging me now. Let say we create a perfect frictionless horizontal plane and we put an object there. Is there a chance it might start moving depending on where we conduct the experiment or the Earth's shape and density distribution forbid this to happen anywhere on Earth?

• – Qmechanic Sep 18 '18 at 12:55
• This is why I love StackExchange! – Kevin Sep 18 '18 at 16:45

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 $\vec{g}+\omega^2 \vec{r}$ at each point. That is exactly what happens to planets in reality while they are still liquid.