Physics

The pendulum

Why the length decides the swing and the weight does not.

Two pendulums of very different weight on rods of the same length, swinging together with their speeds plotted beneath them.

A pendulum's period depends on its length and on gravity, and not on the mass hanging off it — a heavy bob and a light one on the same string keep the same time. For small swings it barely depends on how far it swings either, which is what made it a clock.

QuantityHow it is worked out
Period2π × √(length ÷ gravity)
Quadrupling the lengthdoubles the period

Two pendulums of very different weight on rods of the same length is the first scene in the app, and the point of it is that they stay together. Make one four times as long and it takes twice as long to come back.

Open the pendulum scene in the app to watch this one run.

The rest of it