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Kater's Reversible Pendulum
Plate 001 Physics Poster
Plate 1 speaks for itself: “Flip it. Same beat. That's g.”
The Physics
A compound pendulum with two knife-edges swings with the same period about either edge only when the edge separation equals the length of the equivalent simple pendulum. Kater used this to measure g without needing the centre of mass or the moment of inertia.
g = 4π² (h₁ + h₂) / T² (when T₁ = T₂ = T)
- g: local gravitational acceleration, m s⁻²
- h₁, h₂: distances from the centre of mass to each knife-edge, m
- T: common period about either edge, s
When both edges beat alike, the gap is the length. London, 1817–18: standard g = 9.80665 m s⁻² gives T ≈ 2.006 s for a 1 m equivalent length.
Sources
- H. Kater, Phil. Trans. R. Soc. 108, 33 (1818).
On the poster
Plate 001, “Kater's Reversible Pendulum”: the pixel-art plate with its slogan “Flip it. Same beat. That's g.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.
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The physics
Equations
| Symbol | Meaning | Unit |
|---|---|---|
| \(g\) | local gravitational acceleration | \(\mathrm{m/s²}\) |
| \(h_1, h_2\) | distances from the centre of mass to each knife-edge | \(\mathrm{m}\) |
| \(L\) | distance between the knife-edges (length of the equivalent simple pendulum) | \(\mathrm{m}\) |
| \(T\) | common period of oscillation about either knife-edge | \(\mathrm{s}\) |
| \(T_1, T_2\) | periods about each knife-edge | \(\mathrm{s}\) |
Field notes
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