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