An introduction to physics in the context of everyday objects.

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From the course by University of Virginia

How Things Work: An Introduction to Physics

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An introduction to physics in the context of everyday objects.

From the lesson

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

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

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

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

Â In fact, that it's horizontal and motionless.

Â But the real answer to that question is more subtle.

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

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

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

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

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

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

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

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

Â What seesaws do, do, however. Is rotate.

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

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

Â spinning in place. And see-saws.

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

Â skater exhibits translational inertia. The inertia of going places.

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

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

Â external forces, moves at constant velocity.

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

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

Â When they're rotating, they continue to rotate.

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

Â the Newton's first law of rotational motion.

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

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

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

Â That law has a couple of extra words in it.

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

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

Â What can you do? Rotational motion simply is more

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

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

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

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

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

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

Â a fixed axes turning equal amounts and equal times.

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

Â I described translational motion and identified several physical quantities

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

Â position and velocity. In describing rotational motion, there are

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

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

Â but there, it's technically called angular position.

Â And there is a physical quantity describing how angular position changes

Â with time, and it's called angular velocity.

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

Â 1st, angular position. Angular position is an objects

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

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

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

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

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

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

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

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

Â quantitatively, those various other orientations?

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

Â direction. You need a vector.

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

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

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

Â the orientation that you're trying to describe.

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

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

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

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

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

Â This is 90 degrees. And so is this.

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

Â positions. We need a direction as well.

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

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

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

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

Â So this. Is 90 degrees about a vertical axis.

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

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

Â axis. How do you distinguish them?

Â Well, physicists and mathematicians distinguish them Using a convention known

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

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

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

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

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

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

Â degrees. Downward.

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

Â other way. My thumb is now pointing up, this

Â orientation this angular position is 90 degrees up.

Â So the ambiguity is solved by the right hand rule.

Â 90 degrees down. And 90 degrees up.

Â How about this? That is 90 degrees toward you.

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

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

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

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

Â 270, 360. Another possible unit of degree is the

Â rotation. Full rotation: This is zero, quarter

Â rotation, half, three quarters, full rotation.

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

Â to describe angles, is neither of those two.

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

Â rotation where pi is the mathematical constant.

Â Three point one four one five nine and so on.

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

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

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

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

Â as. 90 degrees down.

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

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

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

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

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

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

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

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

Â changing with time, so my angular velocity is zero.

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

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

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

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

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

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

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

Â Alright, I could show you 90 degrees toward you.

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

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

Â the point. That angle velocity describes how an

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

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

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

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

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

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

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

Â amounts in equal times as having constant angular velocity.

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

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

Â other task. Which is identifying the external

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

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

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

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

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

Â torques. But just so that you know what a torque

Â is. Let me show you what happens when I exert

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

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

Â And suddenly, it changed it's angular velocity.

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

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

Â obeying Newton's first law of rotational motion.

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

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

Â following Newton's first law of rotational motion.

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

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

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

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

Â to rotate steadily? Turning once every, approximately 24

Â hours. The Earth is rotating because it exhibits

Â rotational inertia. It's experiencing essentially no torques,

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

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

Â external torques, so it rotates with constant angular velocity.

Â That angular velocity is approximately one rotation per 24 hours.

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

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

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

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

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

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

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

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

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

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

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

Â And now it's once again rotationally inertial.

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

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

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

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

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

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

Â rotating in the absence of twists. They keep going.

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

Â rotation isn't possible, because during the rotation.

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

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

Â seesaw. It twists the seesaw and therefore takes

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

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

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

Â Are a subject for the next video.

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