Because of the spin of the earth, we are in a rotating frame of approximately constant angular velocity (2pi/1 day).

Like any accelerating frame, this causes 'fictitious forces' relative to a (clasically) inertial frame. E.G. Being a car that makes a fast right, you feel pushed to the left.

For a stationary object (e.g. A wang hanging from a be-doublechaired individual) in a rotationing frame, the equation of motion in this frame is nicely pretty simple as;

Now, as we expect, for a hanging object, like a pendulum, or a wang, will hang in the direction of the field.

For us the direction of this field is only concerned with gravity (i.e. that is the only inertial force -which isn't a force of constraint from the bonds in the molecules in your wang - One could involve tension in the calculation and get the angle, but this is a forum post and I'm sure you don't care))

This g* is in the same direction as the wang hang.

This image of the earth (Credit: NASA), shows the position of the wang, r, and the angular velocity vector ω (this is an "axial" vector so you are spinning around the arrow), it is not hard from here to compute what we need. (Note that real g is in the same direction as r (negative, of course))

Computing the cross products, we obtain,

Visually,

The difference is exaggerated, but as you can see, theta* does not point to the center!

Despite the difference in the angle being small, the difference in position, when you eventually burrow through the earth to give it one, will be sufficient enough for you to miss the hidden womb of immortality.