Maximum Speed of Rotation of Plane of Oscillation of Foucault's Pendulum

Theorem

Let $P$ be a Foucault pendulum.

The maximum angular speed of the plane of oscillation of $P$ occurs at Earth's poles.

Proof

From Angular Speed of Rotation of Plane of Oscillation of Foucault's Pendulum, the angular speed $\alpha$ of the plane of oscillation of $P$ is given by:

$\alpha = \omega \sin \lambda$ where:

$\lambda$ denotes the latitude on Earth at which $P$ is located

$\omega$ denotes the angular speed of rotation of Earth.

So $\size \alpha$ reaches its maximum when $\sin \lambda = \pm 1$.

That is, when $\lambda = \pm 90 \degrees$.

This happens at Earth's poles.

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Foucault's pendulum
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Foucault's pendulum