Extra-terrestrial pendulums

Post date: Jan 13, 2016 9:44:47 PM

Pendulums (or pendula) work by converting gravitational potential energy to kinetic energy and back again. We can use them for timing because the period of a simple pendulum (how long it takes the pendulum to get back to its start place) depends on only two things: how long the pendulum is and how strong gravity is. It might surprise some of you that your mass or how high you swing does not make a difference: if you don't believe me go to a park and time yourself on the swings!*

If we make the string shorter the period will get shorter (it takes less time for the pendulum to complete one swing). You can try this simply by having some keys on the end of a string and shortening the length.

The effect of weaker gravity is that the period gets longer (it takes more time for the pendulum to complete one swing): so a pendulum on the moon would run slower than a pendulum on the earth as gravity is stronger on earth. As Jupiter is much more massive than the earth and moon, a pendulum on Jupiter would run very quickly!

I won't go into the details of the pendulum, which is covered in lots of places (e.g wikipedia), but want to show some fun animations comparing different length pendulums on the earth, moon and Jupiter.

This table is full of animated gifs and can take a while to load.

If all nine animations aren't there then refresh with F5.

We can see that the shorter the pendulum the shorter the period (top row). Also a larger gravity means a shorter period too.

If you're interested in how I generated these images or want to make your own pendulum then hit the link to see the source code.

* there is a small dependence on the period on how big the swing is which increases the period only very slightly - I've not included this here in my calculation and have worked this out for small angles only.