I heard a scientist say once, that because we live in a gravitational field, when we walk our heads travel a?

Question

little bit faster than our feet. I dont get it.

Answer 1

A gravitational field is generated by the Earth. Since our heads are further away from the Earth than our feet, they experience a gravitational effect slightly less than that experienced by our feet. Einstein showed that clocks at higher gravitational potential tick slower. Therefore when you walk your feet and head travel the same distance, but our heads do it in less time. Therefore since velocity = distance / time they must be travelling at a higher velocity than your feet.

Answer 2

Actually, it's because we live on the surface of a sphere.
When you move horizontally, you are actually moving on an arc of a Great Circle. In order to remain upright, your head has to move through the same angle as your feet. call that angle a. On an arc,
a = D/R d/R for your feet, or Df = Ra. since your head is some distance h above your feet Dh = (R + h)a for your head, so
Dh - Df = Ra + ha - Ra
Dh - Df = ha
We don't notice this, though, because the angle a is really, really small.