✓ Sources checked · 10 September 2026 · View verification
A compound pendulum is a rigid body swinging under gravity about a fixed horizontal pivot axis. It is also called a physical pendulum.
By Matan · Updated
Small-angle period
Let d be the pivot-to-centre-of-mass distance and Ip the moment of inertia about the pivot axis. The restoring equation is Ipθ″ = −mgd sin θ. For small angles in radians, sin θ ≈ θ and P = 2π√(Ip/mgd). The pivot is the centre of suspension; it is not generally the centre of oscillation. [1]
Worked uniform rod
A slender uniform rod of length 0.90 m pivots about one end in a vertical plane. With Ip = mL²/3 and d = L/2, P = 2π√(2L/3g). Using g = 9.8 m/s² gives 1.55 s. Multiplying all its mass by the same factor does not alter this ideal period because mass cancels.
Geometry matters
The body need not be a rod; any suitable rigid mass distribution can form a physical pendulum. A stable hanging equilibrium requires the centre of mass below the pivot. At large amplitudes the small-angle period is insufficient. Friction, flexibility and drive mechanisms can also change the motion. The rod is an illustrative ideal model.
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How this article was checked
Sources checked; calculations checked where shown. The definitions, model assumptions and main explanatory claims were cross-checked against the sources below. Worked-example arithmetic and units were checked separately. These examples are illustrative calculations, not experimental measurements.
Source cross-check and editing assisted by AI. No independent human scientific review is recorded for this revision. The check applies to the version dated 10 September 2026; it is not a guarantee that every possible interpretation is correct.
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Sources and further reading
- OpenStax: Physical pendulums — Physical pendulums.
Cite this article
Matan. “Compound pendulum.” Your Physicist. Originally published 2023-03-17; updated 2026-09-10. https://your-physicist.com/compound-pendulum/
Revision history
: Added the small-angle period and rod example; corrected the identification of the pivot with the centre of oscillation. Added linked sources and a transparent verification record.
