Swingrod

Meet Swingrod, a wooden ruler hanging from a pin who swings without any string at all.

A simple pendulum puts all its mass in one small bob. A real object spreads its mass out, so it is called a physical pendulum. Its period depends on its moment of inertia I about the pivot, its mass m, and the distance d from the pivot to its centre of mass.

For a thin rod of length L hung from one end, I = ⅓mL² and d = L/2, so the period becomes T = 2π√(2L/3g). A 30 cm ruler swings with a period of about 0.90 s. A simple pendulum with a 30 cm string would take about 1.10 s.

The ruler is faster because part of its mass sits close to the pivot, where it barely needs to move.

Physical pendulums are used to measure moments of inertia. Engineers hang a part from a pivot, time its swing, and work out I from the period. The same idea keeps the swinging legs of walking animals in a natural rhythm.