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#### 地球自转

Turn of the Earth

[音乐]
[MUSIC PLAYING]

Hi.

I’m Aaron Johnson, a PhD student in the Department

of Aeronautics and Astronautics here at MIT.

And it’s about 2 o’clock in the morning.

We’re in the library, but we’re not working on homework

or not working on a project.

We’re actually proving that the Earth is rotating around

on its axis.

How are we doing that?

Not a light task, I know.

We’re using a 160-year-old device

called a Foucault’s pendulum that we built here

this evening.

So we’ll show you how we built it, how it works,

and like I said, prove that the Earth really

is spinning around.

And so in the words of Foucault himself,
“邀请你来看看地球的自转”
"You are invited to come see the Earth turn."

[INAUDIBLE] is off getting ready for our demonstration.

But how exactly is this going to work?

I mean, how can a Foucault’s pendulum

show that the Earth is rotating around on its axis?

Let’s take a look.

The pendulum is composed of two parts.

There’s a long string, or wire in our case,

with a bob at the end, a heavy weight.

When you start it swinging, a pendulum

swings back and forth until acted upon by an outside force.

This is called inertia.

A Foucault’s pendulum, if left for a long time,

will appear to precess, or rotate.

So if we look at the pendulum from the top,

you would start swinging like this.

And then in the Northern Hemisphere,

after time, it will appear like this, and after more time still

like this.

It’s appearing to precess clockwise

in the Northern Hemisphere.

It’s opposite in the Southern Hemisphere.

So what if we have a pendulum at the North or South Pole?

On this spot, the Earth is twisting,

and that includes the pendulum building.

But the pendulum doesn’t actually move.

So while the pendulum appears to rotate

to an observer in the building, it’s

actually the building turning while the pendulum stays

in the same position.

The pendulum precession period is 24 hours.

What if the pendulum is at the Equator?

This spot on Earth isn’t twisting,

but it’s traveling eastward on Earth’s surface.

Here, the pendulum won’t precess at all.

So these are the two limiting cases.

At this spot on Earth, there is twisting and traveling

eastward.

The pendulum will show this twisting motion, but not

the traveling component of the motion.

As a result, the precession period

will be greater than 24 hours.

There’s a simple formula that lets us find the angular

velocity of our pendulum, represented by omega,

in degrees per day.
w等于360乘以纬度的正弦值
Omega is equal to 360 times the sine of the latitude.

Here in Boston, our latitude is 42.36 degrees North.

So this gives us an angular velocity

of 242.56 degrees per day.

This tells us that our pendulum will precess

10.1 degrees every hour.

This is called the Coriolis effect.

Looking from the top down, pendulums in the Northern

Hemisphere precess clockwise, while pendulums in the Southern

Hemisphere precess counterclockwise.

This has effects on Earth that we can see every day.

Take hurricanes and typhoons, for example.

If we have little bits of wind in the Northern Hemisphere

rotating clockwise, we’re going to get an overall rotation

that’s counterclockwise.

So hurricanes and typhoons in the Northern Hemisphere

rotate counterclockwise.

In the Southern Hemisphere, the opposite is true.

Hurricanes and typhoons rotate clockwise.

Many people think that the Coriolis effect also causes

the water in your toilet bowl to rotate counterclockwise

in the Northern Hemisphere and clockwise in the Southern

Hemisphere.

It’s not really true.

The Coriolis effects are there, but they’re so small

that they’re really overwhelmed by other factors,

such as which way the jets in the toilet are pointing

and how the bowl was filled.

So it’s, unfortunately, not true.
[音乐]
[MUSIC PLAYING]

When we start our Foucault’s pendulum,

we need to make sure not to put any sideways motion on it.

Otherwise, we’re going to see that motion, and not

the rotation of the Earth.

So we’re going to start our pendulum the traditional way.
[音乐]
[MUSIC PLAYING]

We got the pendulum swinging, but it’s

going to take a lot for there to be any visible precession.

So let’s skip ahead one hour.

In one hour, the pendulum has precessed about 10 degrees.

But we can also see that its amplitude

is smaller than before.

This is due to damping.

We used a heavy bob and a long wire

to reduce the effects of damping,

but you can never completely eliminate them.

Foucault’s pendulums that you see in science museums have

an electromagnet that gives the wire a kick each swing

and keeps the pendulum swinging.
[音乐]
[MUSIC PLAYING]

There’s also a bit of sideways oscillation in the pendulum.

You can see it traces out a narrow ellipse.

This is likely because the wire is made of many smaller

wires twisted together, and then as [INAUDIBLE] the tension,

it tends to untwist a bit.

This introduces a sideways torque,

leading [? through ?] the elliptical motion.

However, we can still clearly see

the precession of the pendulum, and thus

the rotation of the Earth.

Ah.

Well, I’d say with that experiment

we proved that the Earth really is

rotating around its axis, which is what we hoped to discover.

So I guess that’s good.

Not bad for a night’s work.

But I really think I’m going to head out and get

some sleep now.
[音乐]
[MUSIC PLAYING]

LD