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Foucault Hoodie

THE FLOOR TURNS UNDER ME | Pixelated Physics

\[\Omega = \omega_\oplus\sin\phi\]
$54.99 USD
$54.99 USD
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Can a pendulum prove the Earth spins? In 1851 Léon Foucault hung one in Paris and watched its swing plane slowly turn. The rate is Ω = ω⊕ sin φ at latitude φ, so a full turn takes one sidereal day at the poles, about 31.8 hours at Paris, and never happens at the equator. Black pixel-art hoodie; equation, symbols and sources in the physics panel below.

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Details

Size & fitS–5XL

Unisex Heavy Blend hoodie (Gildan 18500), classic fit.

SizeWidthLengthSleeve
S202733.5
M222834.5
L242935.5
XL263036.5
2XL283137.5
3XL303238.5
4XL323339.5
5XL343440.5

Measurements in inches. Width and length ±1 in, sleeve (from center back) ±0.75 in.

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Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

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The physics

The swing plane of a Foucault pendulum appears to turn because the floor rotates with the Earth underneath it. The turning rate is the Earth's rotation rate times the sine of the latitude.

In 1851 Léon Foucault hung a long pendulum in the Panthéon. Its swing plane slowly turned.

Relative to the ground the plane precesses at Ω = ω⊕ sin φ. At Paris (φ ≈ 48.85°) that period is T = 2π/|Ω| ≈ 31.8 hours.

At the equator sin φ = 0 so Ω = 0: the plane does not turn. At the pole |Ω| = ω⊕ and the plane turns once per sidereal day.

On the hoodie the filled star-rosette is the ground track of a precessing swing — petals of successive azimuths.

The floor is the turntable. The pendulum just keeps swinging in an inertial plane.

Equations

\[\Omega = \omega_\oplus\sin\phi\]
\[\dot\theta = -\omega_\oplus\sin\phi,\qquad T = 2\pi/|\Omega|\]
SymbolMeaningUnit
\(\Omega\) angular rate of the swing-plane precession \(\mathrm{rad/s}\)
\(\omega_\oplus\) Earth sidereal rotation rate (7.292115\times10^{-5} rad/s) \(\mathrm{rad/s}\)
\(\phi\) geographic latitude \(\mathrm{rad}\)
\(\dot\theta\) rate of change of the swing azimuth \(\mathrm{rad/s}\)
\(T\) period for a full 360° precession of the plane \(\mathrm{s}\)

Sources

  1. Foucault (1851) Démonstration physique du mouvement de rotation de la Terre, Comptes rendus
  2. Halliday, Resnick & Walker, Fundamentals of Physics, Ch. on non-inertial frames / Foucault pendulum
  3. Wikipedia, Foucault pendulum

Source Foucault, L. (1851). Démonstration physique du mouvement de rotation de la Terre au moyen du pendule. Comptes rendus hebdomadaires des séances de l’Académie des sciences, 32, 135–138.

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