Centripetal force and latitude?

Question

Wherever you stand on the Earth, you travel in (very nearly) circular motion with a period of 1 day. This requires a centripetal force directed towards the nearest point on the Earth's axis.
Wherever you stand on the Earth, the force of gravity is (very nearly) in the direction of the center of the Earth. NOT towards the nearest point on the axis unless you're on the equator.

Suppose you're at 40 degrees north latitude. Gravity is at a 40 degree angle from the direction of your acceleration. The normal force from the ground is directly opposite gravity (normal to the surface). The rotation of the ground below you and air around you creates friction towards the east, tangential to the circle. 
What force adds the missing northerly component to your acceleration?

? · Accepted Answer

Normal force from the ground is not directly opposite gravity, but aligned with the vector sum of gravity and the centripetal acceleration r*w², where r = R*cosΘ, the latitude.  This vector sum is aligned with the direction of gravity only at the equator or one of the poles.

? · Answer

I am not sure what you mean by "Gravity is at a 40 degree angle from the direction of your acceleration".

Gravity is the attraction between two objects of mass. This force acts between the object's center of masses.

It does not matter where you are on earth, earth is relatively spherical and therefore has the same gravity everywhere.

Since gravity is a centripetal force it always acts radially INWARD.  
When you do not need the centripetal force, gravity acts on you the same way.
The way earth moves does not limit gravity's effect on you.

Centripetal force and latitude?

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