Elastic-wave propagation and the Coriolis force

In a coordinate system fixed with respect to the rotating Earth, the Coriolis force deflects an object sideways relative to its direction of motion. A beautiful demonstration of that effect is the Foucault pendulum, illustrated in figure 1a. As the long pendulum rocks back and forth, the Coriolis force deflects it the same way on both the forward and reverse swings—to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. The net result is that the pendulum’s plane of oscillation rotates clockwise in the Northern Hemisphere, a change evidenced in figure 1a by the little cylinders that the pendulum has knocked down.

The time rate of change of the oscillation direction is given by ϕ̇=−Ωcosθϕ̇=−Ωcosθ, where, as illustrated in figure 1b, Ω is the rotation rate of Earth and θθ is the colatitude—that is, the angle between the local vertical and Earth’s rotation axis. The minus sign arises because the pendulum maintains its oscillation direction as Earth rotates under it. As a consequence, the pendulum’s direction of oscillation rotates in the sense opposite that of Earth’s rotation, a result most readily visualized by imagining the pendulum to be at the North Pole.