Frictionless body on Earth's Surface

[DBirk]

Homework Statement

Will a frictionless body placed on the Earth move, and if so, describe it's path and acceleration.

Homework Equations

I was given no equations, but I believe that coriolis and centripetal forces would act on the body.

The Attempt at a Solution

I assume that we have to assume an initial velocity of 0 relative to the earth. However, from an external reference frame, the body would appear to be moving as a point on the earth. At the equator this would be approx 1040 mph. However, at latitude angle φ this would decrease as you move towards a pole to cosφ.
The coriolis acceleration, centripetal acceleration, gravity and a force normal to the Earth's surface would act on the body. I assume that gravity and the force normal to the Surface would cancel each other out, but I am not certain. I am having trouble identifying an equation that would capture all of these forces on the body.

 

[haruspex]

You need to allow for the actual shape of tne Earth, i.e. not as a sphere.
Or just consider an object that exists on the Earth's surface and does behave pretty much as frictionless. Can you think of anything?

 

[DBirk]

I can only think of fluids as such, water and atmosphere. Those have different behaviors though.
One man-made object that approaches frictionless would be a mag-lev train.
Similar question, would a mag-lev be (slowly) induced into movement by coriolis or other rotational Earth force if it was left stationary?

 

[haruspex]

I can only think of fluids as such, water and atmosphere. Those have different behaviors though.
One man-made object that approaches frictionless would be a mag-lev train.
Similar question, would a mag-lev be (slowly) induced into movement by coriolis or other rotational Earth force if it was left stationary?

I was thinking of a boat.