Fizzix Phriday: Pedants and PendulumsFriday, March 30, 2012 at 04:23 PM
Today is Friday, and the first of a series of posts that will happen on random Fridays as I decide upon them, known as Fizzix Phridays (the title is a slight shout-out to my high-school physics teacher, who would insist that "Fizzix is phat, and fizzix is phun"). Today I'm going to discuss something that seems inherently simple, but actually has a lot of cool things to know about: pendulums.
You've all seen pendulums before. Whether it's in those old grandfather clocks, the pocket-watch of a hypnotist, or simply a swing-set, pendulums are a part of everyday life. In fact, a pendulum is basically anything with mass at the end of a linear object which is attached to something that allows it to swing freely. Go make yourself one, I don't care how rudimentary. Have one? Good. Now, lift the mass at the end (called the bob), and let it swing from a very low angle. Pay close attention to how long it takes to return to the point it started. That's called a period. Now, try lifting it much higher, and letting it swing again. Notice something? That's right, the period stays the same. Try switching out your bob—making it more or less massive. The period will still remain the same. Now, if you think about it, this makes perfect sense: gravitational acceleration is the same for all objects (9.8m/s2), so the mass won't change anything. And, if you swing it from a higher point, it will fall faster, meaning that it will cover the distance faster. In fact, the period of a pendulum is dependent on only two things: the length of your string, and the acceleration due to gravity. In fact, the equation relating the period to length and gravity is simply:
T = 2π√l/g
What does this mean? It means that, if you were stuck on a strange planet or moon, you could determine the gravity with only a pendulum and a stopwatch, no advanced machinery required. Which is pretty neat. Something else to know about pendulums: because you let them go from a given height (or, technically, angle), when they swing back then can never go higher than that height; when the go down they accelerate, and when they go up the other side, due to gravity still being the same, they will only make it as far up on that side as you let go from (because gravity initially will only accelerate it to a certain velocity before it starts working against it, which will take the exact same amount of time to bring it back to zero, so it covers the same distance (simplification, but we'll leave it at that)).
Finally, we come to the last neat thing about pendulums for today: the Foucault pendulum. Let's say that you have a pendulum that is free to swing in any direction it likes. You give it an initial impetus, and observe it. Logically, it should simply swing back and forth in the same plane, right? Wrong. Over time, it will slowly shift the plane it's swinging back and forth in, eventually processing 360 degrees. Now, the question becomes: why does this happen? Well, it has to do with the Earth, or, specifically, its rotation. When we have a pendulum set up anywhere on the Earth, we know that the Earth is rotating. As such, there is a Coriolis force. The Coriolis force is somewhat simple to understand. Say that you're on a turntable, at the very center. Now, while it's rotating, you try to walk out toward the edge. As you walk, you feel a force pushing you to the side, which curves your path. Obviously there isn't really a force, it's only a result of your motion outward toward the edge moving you from a zone of slower-moving turntable to faster-moving turntable (as you move out, the section of the turntable you're on will be moving faster, think about it, it makes sense. This is also the same force that sustains hurricanes). Now, this same force will affect the pendulum, because it's moving in this 3-dimensional rotating system. So, this force causes it to move, gradually completely a circle in one sidereal day. So that's also pretty damn cool. With a simple pendulum, you can not only determine the gravity of the planet, but that it's both rotating and the length of the day. Physics has some neat little tricks like that all over the place, ways to determine crazy things using very, very simple equipment and your brain. And that, my friends, is why Physics is the best of the sciences.