Foucault Pendulum

The Foucault Pendulum

In 1851, French physicist Léon Foucault suspended a 67-meter pendulum from the dome of the Panthéon in Paris. His goal: to provide direct, visible proof that Earth rotates. The pendulum swung back and forth in a fixed plane relative to the stars, but because Earth rotated beneath it, observers saw the pendulum's swing gradually rotate clockwise.

This simple yet profound experiment was the first mechanical demonstration of Earth's rotation that didn't require astronomical observations. It captivated the public and remains one of the most elegant physics demonstrations ever conceived.

The Physics of Precession

The pendulum obeys Newton's laws of motion — once released, it swings in a plane determined by inertia and gravity. However, Earth is not an inertial reference frame — it rotates. From the ground, we observe an apparent force called the Coriolis force that deflects the pendulum's swing.

At the North Pole, the pendulum's plane rotates 360° every 24 hours (15° per hour). At latitude $\theta$, the rotation rate is $\Omega \sin(\theta)$, where $\Omega$ = 2π/24 hours. At the equator ($\theta = 0$), there is no rotation. At 45° latitude, the period is approximately 34 hours.

The Coriolis Effect

The Coriolis effect arises in any rotating reference frame. On Earth, it deflects moving objects to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. This affects:

• Weather systems — hurricanes rotate counterclockwise in the Northern Hemisphere
• Ocean currents — large-scale circulation patterns
• Artillery and missiles — long-range projectiles must account for Coriolis deflection
• Foucault pendulum — the oscillation plane precession

The Coriolis force is proportional to velocity, making it negligible for everyday motions but significant for large-scale or long-duration movements.

Why a Long Pendulum?

Foucault's original pendulum was 67 meters long with a 28-kilogram bob. The long length served several purposes:

• Long period — minimizes friction and air resistance per swing
• Heavy mass — reduces the effect of air currents
• Slow precession — makes the rotation observable within hours
• Stable oscillation — maintains a consistent plane of swing

Modern Foucault pendulums often use electromagnetic drives to compensate for energy loss, allowing them to run indefinitely in museums and universities worldwide.