Introduction to Classical Mechanics · Problem 10.21

Relativity (Kinematics) — Morin

Physics — Mechanics · corrections-to-gravity

Problem

A mass is dropped from a point directly above the equator. Consider the moment when the object has fallen a distance

d

. If we consider only the centrifugal force, then you can quickly show that the correction to

g_{\text{eff}}

at this point (relative to the release point) is an increase by

\omega^2 d

. There is, however, also a second-order Coriolis effect. What is the sum of these corrections?