What a physical pendulum is
Unlike an idealized simple pendulum (a point mass on a massless string), a physical pendulum is any rigid body that swings about a pivot point, taking into account how its mass is actually distributed.
The formula
The period of small-angle oscillation is T = 2π√(I / (mgd)), where I is the moment of inertia of the body about the pivot axis, m is the total mass, g is gravitational acceleration, and d is the distance from the pivot to the body’s center of mass.
This formula assumes small oscillation angles and negligible friction at the pivot, standard assumptions in introductory and intermediate mechanics.
Last reviewed August 2026