Kater's Reversible Pendulum

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.