[MUSIC PLAYING] (SINGING) Are you ready?

OK this is a family fact of the matter. We have Stephen Morris, those are his feet. Here he is. He's a physicist at the University of Toronto, and that's his son Arthur. And this fact of the matter is all about swinging, which is pretty common, but has very subtle physics, so Stephen tells me.

Well, the first thing you might think about swinging, it seems obvious that a heavy person should swing faster or slower than a lighter person.

Different somehow, yeah.

Different somehow. Maybe dad would be slow and the kid would be fast. Kids always want to go faster right? But it turns out that the time it takes to swing once doesn't depend at all on how heavy the person is.

Really?

Yeah it's a pendulum. So you're swinging, you're the bob on a pendulum, and it turns out that the period, or the time for one swing, doesn't depend at all on the mass or the weight.

So what does it depend on?

Well, it only really depends on the length of string between, or the length of the chain, if you like, in the swing, between the place where it's held and the center of the ball. OK. So when you're swinging, what matters is the distance from where the chain is attached to your center of gravity, which you can think of as a place somewhere behind your belly button.

Yeah, not the position of the swing itself.

No, but sort of your average position which is where the center of your belly button is. And so it turns out that two people that weigh different things would but have the same belly button position actually swing at the same speed.

So if I'm swinging and I'm really tall, so my belly button is really high, I'll swing--

A little bit faster. So I can demonstrate that. Watch, here's a short swing.

Yeah.

Yeah, and if I lengthen the string.

Oh, yeah.

It goes more slowly. So you see this in some parks have really tall swings and they go slowly, and some have little short baby swings that go fast.

That's very neat, but there's more to swinging than just that.

Oh, there's a lot more to swinging than that. The most interesting thing about swinging is the phenomenon of pumping. Every kid learns how to pump themselves up on the swing.

Like Arthur's doing right now.

That's right he has recently--

Leans back and pumps and actually gets himself going higher and higher.

That's right, so everybody knows how to do this, right? You lean back and forth and back and forth. And what you do is go back and forth like this. But the paradox of it is that, if you think about it, if I take my feet off the ground.

Yup. Right, like this, and I'm not moving at all. And I lean back and forth, right, I don't start swinging at all.

Yeah.

And this is exactly like sitting in your stationary car and pushing on your steering wheel to try and get the car to go, right. It doesn't work. And the reason is, is that the force you exert on the car is equal and opposite to the force the car exerts on you, and those just cancel out and you get nowhere.

That's a Newton thing.

That's a Newton thing. So if my feet aren't touching the ground, there's no way I can exert horizontal force to get going. So how does it work?

Good question.

[LAUGHS]

I'm hoping you have the answer.

I have the answer. Well, it turns out that what you do when you're pumping is you lengthen and shorten the distance between your center of gravity and where the chain is attached. So every time you lean back you lower your center of gravity--

Right.

--and every time you lean forward you raise it. OK. And if the swing is away from vertical, like this, the work you do, the force you exert, has some part that pushes you forward. OK. So what you have to do to pump yourself is to get going.

You've gotta get off the vertical, right?

That's right, you get off the vertical. And then you lean back and forward and back.

And so really, but even though it's off the vertical, all you're really doing is lowering and raising your center of gravity. But it's still kind of a vertical movement.

Well, but the only thing you can exert a force on is the chain, and you can only exert a force in the direction of the chain, because this is the thing that's attached to the earth, right.

Right.

And you have to do tug something--

Something you can push on or pull on.

--in this case. Yeah. So it's easy to demonstrate this. If I hold this, with some length like that, and it's stationary, and if I lengthen and shorten, lengthen and shorten, does not swing. OK? But if I get it swinging and I lengthen and shorten it at just the right frequency--

Oh, yeah.

--I can make it swing higher you see. And so that's what you're doing.

But it's just the right frequency, like if you did it double that speed or something, you wouldn't go anywhere.

That's right. So you have to do it, lean back on one swing and up on the next one, and that's just the right frequency to pump energy in.

And you know, the beautiful thing about that is that kids like your son Arthur do that completely intuitively.

That's right.

They don't sit down and work out equations.

It's like riding a bike. That's right. But the funny thing is, that you're pumping yourself with a force that's actually not in the forward direction, it's actually just pulling yourself up toward the point of support, up the chain.

But there's a little part of that, that gets you going this way.

But it doesn't work unless you're off the center already. So pull here and then you get, then you speed.

Wow. That was great. Thank you Stephen.

Thank you.

You can swing some more if you like.

Yeah.

Stephen Morris is a professor of physics at the University of Toronto. That's his son Arthur, he's in grade two. And this has been a fact of the matter.

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