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This is my talk for the Dunn Middle School graduation ceremony on 2 June 1995, delivered outdoors on the steps of the Middle School. I explain how to do it at the end.

{Hold up the broom.}

People who have never been to a Middle School graduation are possibly wondering "What the heck is he doing with that broom?" And people who have been to past graduations are possibly wondering "What the heck is he doing with that broom?" Let me explain. It's my custom to do a science experiment or demonstration for my graduation speech and then (hopefully) to end with a moral or lesson appropriate to the occasion.

Today I have a stumper with brooms, one of the most important but least appreciated instruments of science. This is a stumper about balance.

Balance is an interesting concept. If you think of a gymnast poised motionless on a balance beam, you might think of balance as something static. Yet we wouldn't ordinarily say that we are balanced on our chairs right now just because we're sitting here. (There are other times when just sitting is a feat, and we might say this!) Balancing is a more dynamic concept. We speak of balance when there's a real chance of falling, and we have to do something not to fall. Balance becomes interesting when it seems something should fall, but it doesn't.

One thing you can do with a broom is to find it's balance point or center of gravity. There's an old technique for this. You put your fingers anywhere near the ends and slide them together. They will meet at the stick's center of gravity.

{Do it with both the walking stick and the broom. Note how the center of gravity of the broom is not in the center. The straw end is heavier.}

When I first saw this years ago, I wasn't impressed. "Of course my fingers will meet in the center." Actually the mechanism of this is quite elegant. The heavier end presses harder on its finger, creating more friction, so the other finger slides easier. But after a while the situation switches, and the roles are reversed.

This sort of correction and over-correction is typical of balance. I've really become aware of this watching my kids learn to drive. They go a bit to the left, so they turn to the right. But they turn too much and overcompensate, so they have to turn back to the left, and so they zig-zag down the road. After a while this becomes second nature, and we forget that we're doing this all the time. The gymnast on the balance beam is also making small corrections constantly, but we don't see it, at least we shouldn't.

There's some interesting tricks and illusions with center of gravity. My favorite is the sky-hook or belt hanger that we made in Tools and Materials class when these 8th graders were in 6th grade.

{Demonstrate the sky-hook.}

The secret is that this only works with belts, and the belt must point backwards. I understand this perfectly with my mind. It's really no different than a c-clamp. But it still seems mysterious when I do it. When kids ask how it works, I just smile and say "Center of gravity, of course" and try to change the subject.

You can balance a broom horizontally by putting your finger at the center of gravity. But you can also balance it on end.

{Do it.}

Notice that my finger is still under the center of gravity. When the broom starts to fall, I move my hand over to keep it under the center, usually a bit too far, just like driving. I overcompensate, so I have to keep moving back and forth.

You can also balance the broom on the straw end, but it's harder because the straw is soft. The straw end is also heavier. This raises a question: how does the extra weight effect the balancing?

So here's my stumper. If I add a real weight to the broom stick, will it be easier to balance if the weight is down close to my hand or up in the air?

{Show both positions, but don't do it yet.}

Think about this for a moment and make a hypothesis. Is it easier to balance with the weight high or low?

I asked this question in class this week and most kids said it will be easier with the weight down low. This makes sense. Microphone stands are heavy at the base, to keep their balance. When backpacking it's a working rule to put the heaviest things at the bottom of your pack, otherwise you'll be top heavy and your pack will swing and throw you off balance as you walk. In general in sports, coaches say to keep a low center of gravity. Let's try it each way.

{Do it, first with the weight up high, then down low. Caution the front rows in case it falls. It should be obvious that it's more stable with the weight high.}

It's clearly easier to balance when the weight is high. Why? My guess is that when the weight is further away, there is more time to respond to changes and more time to restore the balance. When the weight is low and it starts to tilt, things happen too fast. There's no time and no space to get back under the center.

Really this shouldn't be too surprising. Gymnasts keep their arms extended. Tightrope walkers use a crossbar. Think of a circus act. One person balances a pole with a chair on top, and a second person jumps into it. It's more impressive with the long pole, and it's also easier. "Center of gravity, of course!"

Enough classroom stuff. This is graduation for these kids.

I thought of this as a graduation experiment on the first day of our 8th grade trip exactly two weeks ago. Clarin and I went with the 8th grade to my cabin in the Owens Valley Desert on the eastern side of the High Sierra, at the base of Mount Whitney. We struggled with food lists and packing and finishing classwork and yearbook pages. Finally we got under way. Just outside the town of Mohave, my van died. We waited on the highway for an hour until a tow truck came, and there we were, stuck in Mohave, not knowing what was wrong, for an indefinate period of time.

I was starting to feel down. We might be stuck here all night. What could we do? But then the kids made the best of it. I'm sure the girls all wanted to invite the tow truck driver to graduation today. He was cute, and he let them ride in the cab of the truck. And the rest of us were excited because he forgot about the bikes on the roof of the van and took out a string of flags and almost a power line! This was a good beginning.

In Mohave we had fun talking about congressmen (inside joke!) and making the horn sign to the truck drivers and scattering when one truck actually stopped. The repair job turned out to be minor, and soon enough we were on the road again. We got to the cabin before dark. Everything was fine.

On the way out of Mohave, Laurel really startled me by asking if I'd arranged the breakdown on purpose, just to bring us all together as a group. I laughed... actually I was flattered that Laurel thought I knew enough about cars to do that! But Laurel was right. We weren't driving hundreds of miles just to be comfortable. If that was all we wanted, we could have stayed home and rented some movies. We came on our trip to have a great time together in a new and strange place. That's something different.

And so, driving through the desert, I thought about brooms.

Just like it's hard to balance a broom with the weight down low, so it's hard to survive a trip with low expectations. Going that far, with that many people, things will go wrong. But we had a great trip partly because of the hard times. That afternoon in Mohave made us better friends because it made us realize that we had different goals than just comfort or getting there. And that made it easy to keep our own balance with each other.

You 8th grade seniors, remember this as you leave the Middle School and go on with your own lives: that's quite a trip! Keep your goals high. Expect a lot. Adjust your balance when you have to, that's part of the process. And you'll do all right!

## How to do it:

What I used for the speech:

• A Broom, not too shabby
• A 5-10 pound weight with a center hole that fits the broom stick
• Walking stick
• Sky-hook and a belt
• C-clamp

Use a fairly new broom with stiff bristles. Drill a 1/4 inch hole through the broom stick just above the straw and another near the top. Then push a bolt or rod part way through the hole to support a round weight from a barbell set. By moving the bolt from hole to hole, it's easy to place the weight at the top or bottom of the broom stick. You can balance it either way, but it's much easier with the wieght up high.

A knitting needle with a ball of clay for the weight also works well. But I like using the broom.

You can find the center of gravity of a broom by sliding your fingers together. But the varnish on my broom was so rough that it wasn't very interesting to watch. It worked better with a smooth walking stick I had that had a big knot on one end to keep it off balance. Move your fingers fairly fast.

Sky-hooks are a good woodworking project for kids. Trace the shape on 1/4 or 3/8 inch wood (cheap redwood lath works fine), cut it out with a coping saw, and sand it smooth. (I'll scan the plans when I have time.) It really works, but only with a belt. Look at it and you'll see the connection with a c-clamp.