the physical pendulum
A physical pendulum is any real, solid object swinging about a pivot, not just a tiny weight on a string. Think of a baseball bat hung from one end and set swinging, a rocking shop sign, or your own leg swinging as you walk. It extends the pendulum idea to bodies whose mass is spread out rather than concentrated at a single point.
Precisely, take a rigid body of mass m pivoted at a point a distance d from its center of mass, free to swing under gravity. For small angles the motion is simple harmonic with period T = 2 pi sqrt(I / (m g d)), where I is the moment of inertia about the pivot: a measure of how the body's mass is distributed around that axis. The simple pendulum is just the special case where all the mass sits at the end, giving I = m L^2 and d = L, which recovers T = 2 pi sqrt(L/g).
Physical pendulums show up in real clocks, in the mechanics of walking (your leg swings like one), and in the tuning of hanging structures. One point that trips people up: you must use the moment of inertia about the actual pivot, not about the center of mass. The parallel-axis theorem gives you the pivot value from the center-of-mass value plus m d^2.
A uniform rod of length L pivoted at one end has moment of inertia I = (1/3) m L^2 about that end and d = L/2 to its center. Its period is T = 2 pi sqrt((1/3 m L^2)/(m g (L/2))) = 2 pi sqrt(2L / (3g)), a bit shorter than a simple pendulum of the same length.
For an extended body the period uses its moment of inertia about the pivot, not just its length.
Use the moment of inertia about the pivot (via the parallel-axis theorem), not about the center of mass; and small-angle SHM still applies only for small swings.