Say the world is completely flat and devoid of hills and objects?

Question

and I take a cherry and move it from equator to the pole.
It does not require any force or work, does it?

And then moment of inertia of the Earth (with the cherry) will decrese, and the speed of rotation will increase accordingly.

Will kinetic energy of roatation of Earth (with the cherry) increase, remain the same, or decrese?

Answer 1

This is similiar to how ice skaters spin faster as they pull in their arms. Angular momentum is conserved, but rotational kinetic energy is not. Hence, as the system moment of inertia decreases and the rotational speed increases, the rotational kinetic energy increases, which means work was done to make this happen. It takes a bit of work for an ice skater to pull in his/her arms too while spinning. Let L = angular momentum, I = momentum of inertia, E = rotational energy, and ω = angular speed. Then we have:

L = I ω
E = (1/2) I ω²

or

E = (1/2) L² / I

showing the inverse relationship between E and I, if L is a constant.

Answer 2

I assume you mean "smooth" and not "flat" - a smooth and perfect sphere as opposed to a flat world with edges.

As you approach the pole with the cherry, you are bringing more mass towards the axis of rotation, and so the rotation would speed up imperceptibly.

However, talking there would require work.

Answer 3

it will require work and force due to friction

the kinetic energy of rotation of the earth will remain the same

Answer 4

If the earth was completely flat it wouldn't have a pole or an equator!
.

Answer 5

idk well i guest not if i eat it