✓ Sources checked · 10 September 2026 · View verification
Kater’s pendulum estimates local gravitational acceleration by matching small-angle periods about two different knife-edge pivots. The distance between the pivots remains an essential measured length.
By Matan · Updated
Reverse the pendulum
For a physical pendulum, T = 2π√(Ip/(mgd)). In a reversible pendulum with pivots on opposite sides of the centre of mass, adjust the distribution so the two periods match. For unequal pivot-to-centre distances d₁ and d₂, the matching condition gives Icm = md₁d₂ and equivalent length L = d₁ + d₂. [1]
Worked estimate of g
Suppose pivot separation is L = 0.994 m and the matched period is T = 2.000 s. Then g = 4π²L/T² = 9.810 m/s². These are illustrative inputs, not a new measurement of a location. The relevant length is pivot separation, not distance between the movable masses.
Timing error matters twice
Because g is proportional to T⁻², a 0.10% relative timing bias causes approximately 0.20% opposite relative bias in g when L is fixed. Timing several oscillations and extrapolating small-amplitude behavior can reduce errors.
A match needs the right geometry
Equal distances d₁ = d₂ produce equal periods automatically and do not establish the needed inertia condition. Knife-edge geometry, unequal periods, air effects and finite amplitude need correction for precision work. Matching periods about two pivots is not independence from every bob position.
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How this article was checked
Sources checked; calculations checked where shown. Main claims and model assumptions were checked against the references below. Example arithmetic and units were checked separately. Numerical examples are illustrative calculations, not experimental measurements.
Source checking and editing assisted by AI. No independent human scientific review is recorded for this revision. This record applies to the version dated 10 September 2026.
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Cite this article
Matan. “Kater’s pendulum.” Your Physicist. Originally published 2023-03-17; updated 2026-09-10. https://your-physicist.com/katers-pendulum/
Revision history
10 September 2026: Corrected the apparatus, measured length and equal-period condition; removed unsupported Apollo-use claims. Added references and a transparent verification record.
