An introduction to physics in the context of everyday objects.

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來自 University of Virginia 的課程

生活中的物理

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An introduction to physics in the context of everyday objects.

從本節課中

Seesaws

Professor Bloomfield illustrates the physics concepts of rotational versus translational motion, Newton's law of rotation, and 5 physical quantities: angular position, angular velocity, angular acceleration, torque, and rotational mass using seesaws.

- Louis A. BloomfieldProfessor of Physics

How does a balanced seesaw move? The full answer to that question will

require some careful explaining, but a short answer is that a balanced seesaw

rotates steadily about a fixed axis. Now it's tempting to think that I've just

asked a trick question, that a balanced seesaw doesn't move at all.

In fact, that it's horizontal and motionless.

But the real answer to that question is more subtle.

Yes, a balanced seesaw can be horizontal, and it can be motionless.

But it doesn't have to be. What a balanced seesaw does exhibit,

however, is rotational inertia. If I set it spinning, it rotates steadily

about a fixed axis. Up until now, I've talked about a type of

motion that takes you from place to place. So, in the episodes on skating, falling

balls, and ramps. We went somewhere from place to place.

In this episode on seesaws, we don't go anywhere.

Seesaws are installed in playgrounds. And they stay there indefinitely.

What seesaws do, do, however. Is rotate.

So, the world of motion can divide into two main types.

The motion of translation, of going somewhere and the motion of rotation,

spinning in place. And see-saws.

They're about spinning in place. In the episode on skating, we saw that a

skater exhibits translational inertia. The inertia of going places.

And associated with that translational inertia was Newton's first law of

translational motion. Namely, that an object that's free of

external forces, moves at constant velocity.

In this episode on seesaws, we're looking at objects that can exhibit rotational

inertia. When they're at rest, they stay at rest.

When they're rotating, they continue to rotate.

Associated with rotational inertia is another Newton's first law, but now it's

the Newton's first law of rotational motion.

In a draft form Newton's first law of rotational motion states that a rigid

object that is wobbling and that is not experiencing any outside influences,

rotatates about a fixed axis turning equal amounts in equal times.

That law has a couple of extra words in it.

It refers only to rigid objects and objects that are not wobbling.

So Newton's First Law of Rotational Motion has relatively limited applicability.

What can you do? Rotational motion simply is more

complicated than translational motion and therefore the Newton's 1st Law in the

world of rotation is fairly limited. There are lots of things that don't that

don't follow Newton's 1st Law of rotational motion.

>> Because they either change shape, or because they're wobbling.

To perfect the draft of Newton's First Law of Rotational Motion, we need to identify

the external influences, and we need better language to describe rotation about

a fixed axes turning equal amounts and equal times.

I'm going to start with the second task. In the previous episodes.

I described translational motion and identified several physical quantities

that are useful for that description. Among those physical quantities were

position and velocity. In describing rotational motion, there are

analogous physical quantities. There is a physical quantity describing...

(End of transcription.) Angular position. Angular, rotational, it doesn't matter,

but there, it's technically called angular position.

And there is a physical quantity describing how angular position changes

with time, and it's called angular velocity.

So, those are the 2 quantities I want to introduce.

1st, angular position. Angular position is an objects

orientation, and instead of illustrating angular position using the seesaw, I'm

going to illustrate it using my body. So, angular position will describe how I'm

oriented. I'm going to start with a zero of angular

position, which is the starting point, the, the zero.

This will be my 0 of angular positioning, the orientation that we all agree is the

starting point, facing you. If I change my angular position, that

means that I'm facing some other direction, like this or this or like this

and Like that, and so on. Well, how do you describe, technically,

quantitatively, those various other orientations?

How do you do it? Actually, you need an amount and a

direction. You need a vector.

And here's how the vector. [inaudible] So angle position is a vector

quality and here's how it works. First, the amount is an angle.

The angle through which you have to rotate to go from the zero, namely facing you, to

the orientation that you're trying to describe.

For example this, this is the one I'm going to try to describe.

Facing like this. And the angle that I have to rotate

through to go from the zero to this is 90 degrees.

From there to there, that's 90 d-, you know [LAUGH]what, 90 degrees right?.

So this angle position is 90 degrees. But that's not enough.

This is 90 degrees. And so is this.

And so is this, alright? So there are a bunch of 90 degree angles

positions. We need a direction as well.

And the direction. Of an angular position is the axis about

which the rotation occurs. For example, to, to rotate to this 90

degree angular position, I need to rotate about a vertical axis as though I were a

toy top being spun. So I'm being spun, there I go.

So this. Is 90 degrees about a vertical axis.

But there's a ambiguity. This is 90 degrees about a vertical axis.

And so is this. They're both 90 degrees about a vertical

axis. How do you distinguish them?

Well, physicists and mathematicians distinguish them Using a convention known

as the right-hand Rule. And the right-hand rule says that if you

take your fingers of your right hand and curl them in the direction in which the

rotation occurs. For example, if I'm going from this to

this, the rotation is like that. Then look at my thumb.

The thumb of my right hand, points in the official direction of that rotation,

downward. So in going from 0 to this, I rotated 90

degrees. Downward.

On the other hand, if I go from this to this, my fingers have to be pointing the

other way. My thumb is now pointing up, this

orientation this angular position is 90 degrees up.

So the ambiguity is solved by the right hand rule.

90 degrees down. And 90 degrees up.

How about this? That is 90 degrees toward you.

And this is 90 degrees towards me. Final word about angles.

The angle part of anchor position can be measured in various units.

Up until now, I've been using the unit known as the degree.

It's a familiar unit of angle; this is zero degrees, 90 degrees, 180 degrees,

270, 360. Another possible unit of degree is the

rotation. Full rotation: This is zero, quarter

rotation, half, three quarters, full rotation.

(End of transcription.) But the unit that mathematicians and physicists normally use

to describe angles, is neither of those two.

It's the radian. And there are two pi radians in a full

rotation where pi is the mathematical constant.

Three point one four one five nine and so on.

And that is the natural unit of angles. There are reasons why it's particularly

useful in physics. Whether you use it or not, doesn't matter.

Pick your, pick your unit of angle and stick with it.

You're fine. So you can describe this angular position

as. 90 degrees down.

Or quarter rotation down. Or pi over two radians down.

They're all the same. That's angular position, but that by

itself doesn't help us Redraft Newton's first law of rotational motion.

We need to look a little deeper. We have to look at how angular position is

changing with time, because when something is actually rotating its angular position

is evolving, changing with time. And we need the next physical quantity

which is angular velocity. Angular velocity is The rate at which

angular position is changing with time. So right now my angular position is not

changing with time, so my angular velocity is zero.

But if I begin to spin, then my angular velocity is no longer zero.

For example, if I turn like this I am now turning about.

90 degrees per second. And I am, the, the, the same right hand

rule applies. I'm turning such that my fingers curl like

this and my thumb points out. This is an angular velocity.

Of 90 degrees per second down. Also pie over two radians per second down.

Let me stop. Let me show you 90 degrees up, here it is.

Alright, I could show you 90 degrees toward you.

90 , yeah 90 degrees per second toward you but that's, I'm going to run out of

ability to do this. But you get, I hope you, I hope you get

the point. That angle velocity describes how an

object is rotated, that is how fast it's going through angles, and also the axis

about which it's, it's spinning and finally, the right, using the right hand

rule, the specific direction of its spin around that axis.

So you should be able now to distinguish 90 degrees per second down from 90 degrees

per second up. That now, that physical quantity, angle

velocity will be useful in redrafting Newton's first law, rotation motion.

Because we can rewrite the turning about, rotating about fixed axis, turning equal

amounts in equal times as having constant angular velocity.

If I'm turning 90 degrees per second down and staying that way My angular velocity

is constant. Alright, that brings us to this, to the

other task. Which is identifying the external

influences that show up in Newton's first law of rotational motion.

And those external influences are twists. Technically, they're known as torques.

A torque is the[INAUDIBLE], is the influence that causes, that upsets

rotational inertia. And therefore, violates Newton's first law

of rotational measure. We'll, we'll, we'll look more at, at, at

torques. But just so that you know what a torque

is. Let me show you what happens when I exert

a torque on this seesaw. To, to do it, I twist the see-saw.

So I'll grab the see-saw from the front, and I will twist.

And suddenly, it changed it's angular velocity.

It started with an angular velocity of z, of zero, let's get zero there.

And it's now, for the, at present it is a rigid object that's not wobbly, it's

obeying Newton's first law of rotational motion.

But if I come in with an external influence of the right type.

Namely, a torque. While I'm exerting that torque, it is not

following Newton's first law of rotational motion.

It, it changed it's angular velocity. So, we can now state Newton's first law of

rotational motion in all it's glory. A rigid object that is not wobbling and

that is free of external torques rotates at constant angular velocity.

That brings us to a question. What influence or effect causes the earth

to rotate steadily? Turning once every, approximately 24

hours. The Earth is rotating because it exhibits

rotational inertia. It's experiencing essentially no torques,

and therefore, it rotates according to Newton's 1st Law of Rotational Motion,

namely >> It's a rigid object that is not wobbling, it is not experiencing any

external torques, so it rotates with constant angular velocity.

That angular velocity is approximately one rotation per 24 hours.

About the north poles so that the rotational axis points from the center of

the earth up to the north pole and that's the way the earth rotates.

So we see a balanced seesaw is not necessarily motionless or horizontal.

What we can say about that balanced seesaw however, is that it exhibits rotational

inertia. If it's motionless, it remains motionless.

If it's rotating, it continues to rotate. Because it's a rigid object that's not

wobbling, it exhibits a particularly simple type of rotational motion.

Namely, constant angular velocity. So right now, the con, the angular

velocity of this balanced seesaw Is 0. But if I twist it, and during the twist

it's not rotationally inertial and so, I'm violating Newton's 1st Law of rotational

motion by doing the twist, here we go, I'll give it a twist.

And now it's once again rotationally inertial.

It's, it's obeying Newton's 1st Law of rotational motion.

It's a rigid object that is not wobbling, it's free of external torques.

Speaker:so, it rotates at constant angular velocity, apart from some air resistance

problems here. The point is, it's rotating right now, not

because something is twisting it, but because nothing is twisting it.

It is, it is it's nature, and the nature of objects in our universe to keep

rotating in the absence of twists. They keep going.

That's rotational inertia. So, in, in a normal see-saw that perpetual

rotation isn't possible, because during the rotation.

Even when it's balanced initially. It eventually touches the ground.

And at those moments when it touches the ground, the ground exerts torques on the

seesaw. It twists the seesaw and therefore takes

it out of the, out of Newton's First Law of Rotational Motion, violates Newton's

First Law of Rotational Mo-, and new things happen.

And those new things, basically the consequences of torques...

Are a subject for the next video.