# Newtonian Mechanics – Dynamics of an Object Standing Still on a Perfectly Spherical Earth

centrifugal forceequilibriumfree-body-diagramnewtonian-gravitynewtonian-mechanics

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?

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.