The Foucault pendulum is one of the most elegant demonstrations that Earth rotates on its axis. Named after French physicist Léon Foucault, who first publicly demonstrated it in 1851.
The Key Insight:
═══════════════
A pendulum, once set swinging, maintains its plane of oscillation
relative to the FIXED STARS (inertial reference frame).
But we stand on EARTH, which is rotating!
So from our perspective on Earth's surface, the pendulum's
swing plane appears to slowly rotate throughout the day.
Fixed Stars (inertial frame)
↓
┌─────────────────┐
│ Pendulum plane │ ← Stays constant
│ ◉ │
│ /|\ │
└─────────────────┘
↑
Earth rotating beneath
The Rate of Rotation:
════════════════════
ω = 15° × sin(latitude) per hour
• At the POLES (±90°): Full rotation in 24 hours
sin(90°) = 1, so 15°/hour × 24h = 360°
• At the EQUATOR (0°): No rotation at all!
sin(0°) = 0, so 0°/hour
• At PARIS (48°): About 32 hours for full rotation
sin(48°) ≈ 0.74, so 11.1°/hour
Precession Period Formula:
T = 24 hours / |sin(φ)|
Where:
• T = time for one complete rotation
• φ = latitude (in degrees)
• 24 = hours in one sidereal day
┌─────────────────────────────────────────┐
│ Latitude │ sin(lat) │ Period (hours) │
├───────────┼──────────┼─────────────────┤
│ 90° │ 1.00 │ 24.0 │
│ 60° │ 0.87 │ 27.7 │
│ 45° │ 0.71 │ 33.9 │
│ 30° │ 0.50 │ 48.0 │
│ 15° │ 0.26 │ 92.9 │
│ 0° │ 0.00 │ ∞ (never) │
└─────────────────────────────────────────┘
The Coriolis Effect
═══════════════════
On a rotating sphere, moving objects appear to curve.
In the Northern Hemisphere: curves RIGHT ↷
In the Southern Hemisphere: curves LEFT ↶
This same effect causes:
• Weather systems to spin (hurricanes, cyclones)
• Ocean currents to curve
• Artillery shells to drift
• And pendulums to precess!
The Pendulum's Perspective:
Earth View: Space View:
═══════════ ══════════
"The pendulum "Earth rotates
rotates clockwise" under the fixed
pendulum plane"
↓ ↓
╭─────╮ ╭─────╮
│ ↻ │ │ · │ ← fixed
╰─────╯ ╰──↺──╯
↑ ↑
We see this Reality