As part of my “What is Possible?” class (supposedly eighth grade American History), we spend more than a month studying the time between the Magna Carta and the ratification of the United States Constitution, learning about some of the changes that made possible the way of seeing the world underlying the Constitution.
We had talked about Copernicus and then did a day-long immersion in Kepler’s three laws of planetary motion, especially how the speed of orbiting bodies changes, accelerating towards perihelion, slowing on the way out to aphelion. Student A related it to being like the ups and downs of a roller coaster.
The next day we were learning about Galileo and his experimental approach and how he needed a way to measure time. We experimented with an eight-foot pendulum hanging from the middle of the classroom’s ceiling. Through a lovely feedback spiral involving teacher/pendulum/students, the students led themselves into the unexpected experience that how far back you pull the pendulum for its initial release makes no difference to its period, the time it takes to swing back and forth. This was especially dramatic with the 8 foot pendulum. Ten swings took 33 seconds, whether it swung through a one inch arc or a 6 foot arc. After class, Student B was actively trying to make sense of this. (Student A hung around.) She told how she used to play a game of trying to run around her bed in the same amount of time, no matter how far away from it she was. Right next to the bed she could walk but she would have to run further out. She was trying to use those experiences of short/slow coming out the same as long/fast to help her relate to the pendulum.
I pointed out that her running around her bed gave her a unique perspective on the pendulum and how each of us has accumulated unique experiences that give us special insights into different aspects of the world. I included Student A by mentioning how he, an athletic kid, related the orbit of the planets to the roller coaster. That he, for example, might have spent many hours learning how to toss a hatchet so that it stuck into a tree. He confirmed that he had. Those hours of playing with heft would lay down pathways that give him a unique perspective on rotating objects. Each one of us brings unique experiences that allow unique insights, valuable to us all.
The next day, some of the kids asked what would happen if we changed the length of the string. I replied, “What would Galileo say?” One student tried predicting the conclusion that Galileo would have drawn about gravity. But I said, “No, what would Galileo say if you asked him that question about changing the length of the string?” They didn’t understand. “He would say, ‘Let’s try it and find out’.” So we started shortening the string, timing ten oscillations of a gradually shortening pendulum, the time growing shorter and shorter to the fascination of the kids. (Later, one of the students asked what would happen if the mass of the pendulum changed. I said, “What would Galileo say?” and they all shouted “Let’s try it,” and they set off on another investigation.)
But back to the shortening of the pendulum and the speeding up of its swing. We kept shortening and timing it. We reached the length where ten swings took ten seconds—like a ticking clock. And we kept going. I had to get up on a chair to shorten it again and I hear Student B excitedly asking “Is this like the orbits of the planets?” (We had made a graph of planetary distance vs. period while studying Kepler.) “That like…like the long pendulum is like Neptune and the short pendulum is like Mercury and it’s like the planets are on strings and the short string planets have shorter periods?”
I get down on my knees in front of her and touch my forehead to the floor three times. ”You have just done what the genius of Newton did. You saw a connection between the behavior of the swinging pendulum and the behavior of the orbiting planets and are now wondering if a deep pattern underlies them both.”
Leave a Reply