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

Why do the riders' weights and positions affect the seesaw's motion?

Â The short answer to that question is that they affect the net torque on the seesaw,

Â and therefore the seesaw's angular acceleration.

Â In most cases, the riders of a seesaw position themselves so the net torque on

Â the seesaw is 0 or very nearly 0. As a result, the angular acceleration of

Â the seesaw is either 0. That is, its coasting rotationally.

Â Or it's just got the smallest amount of angular acceleration.

Â Well, that then requires a longer explanation.

Â How does that come about? You put riders on the seesaw; why don't

Â they produce enormous net torques? So we know that if we put one rider on the

Â seesaw, that rider's, because of the rider's weight, the rider pushes down on

Â the seesaw over here, on the, on your left...

Â [unknown] That's to the lever arm from the pivot.

Â It produces a torque and boom, the seesaw undergoes rapid angular acceleration such

Â that, that rider drops to the ground. But what if we put two riders on the, on

Â the seesaw simultaneously? And what I'm going to do is I'm going to

Â position them very carefully. And look.

Â The seesaw is experiencing very little angular acceleration, so the net torque on

Â it is either zero or very near zero. How did that happen?

Â Aren't these riders producing big torques on the seesaw?

Â There are two of them. >> Glad you asked that question.

Â Here's the story, this is now the longer explanation to the question that's

Â prompted this video. That rider because the rider's weight is

Â pushing down on the board, over here to your left, the lever arm that, that riders

Â force is using to produce a torque, points towards your left.

Â Here it is, and using the right hand rule now, we can see the direction of the

Â torque produced by that rider. The torque, we follow the lever arm and we

Â roll, I roll my finger down in the direction of the force and my thumb is

Â pointing toward you. That is the direction of a torque,

Â produced by this rep, a, this seesaw rider.

Â Let's come over to this seesaw rider. I need my right hand again.

Â I can't swap hands or I'll get the wrong answer.

Â So, that rider by virtue of his or her weight, is pushing down on the seesaw

Â board. The lever arm with which that rider is

Â producing a torque now, points to your right.

Â So, there it goes. And now I turn my, my index finger in the

Â direction of the force. And lo and behold, the torque produced by

Â that rider is away from you. So these two torques are in opposite

Â directions. This rider is producing a torque toward

Â you. This rider is producing a torque away from

Â you. When we add those two torques, and they

Â are the two torques acting on this seesaw, they sum to zero or very nearly zero.

Â And that's how it is that when I let go of this board and allow it to show you its

Â angular acceleration There's almost zero. If there is a little bit, and there is, I

Â can adjust the distance of one of the riders from the pivot.

Â This riders producing a little too much torque.

Â And now I, I move it toward the pivot, still a little too much torque.

Â So I move it a little closer to the pivot, and now That rider's producing almost jjst

Â the right torque. Let me move the rider in a little closer

Â and now this rider's producing too little torque.

Â I have been, I have adjusted the rider's positions, that is the lever arms they're

Â using, to show you that we can go all the way from.

Â Almost perfect balance, and I'll talk about balance in a minute, with that rider

Â dominating a little bit, to almost perfect balance with that rider dominating a

Â little bit. And everything in between, including in

Â principle, perfect balance where there's zero net torque on the seesaw.

Â >> Actually, balance is an interesting concept.

Â The balance that we talk about in the context of a seesaw, and many other

Â objects that teeter back and forth like a seesaw, is a situation where gravity

Â produces no torque on the object. So, when this seesaw is balanced It's

Â experiencing 0 torque due to gravity. I can come in and, and change things.

Â I'm, I'm here, very carefully adjusting positions in order to try get this

Â situation. This seesaw is almost perfectly balanced.

Â Meaning it's experiencing almost 0 torque due to gravity.

Â And that is the normal situation for a seesaw, and riders.

Â They like that situation because a balanced seesaw is free of torque, this

Â assumes nothing else is exerting torques on it, and it will turn at constant

Â angular velocity. It is an object that obeys Newton's First

Â Law of Rotational Motion. And it's not wobbling, it's rigid,

Â assuming the riders don't change their positions.

Â And therefore, in the absence of any torque, and there's no gravitational

Â torque on a balanced seesaw, it turns a constant negative velocity.

Â So, the, the reason the riders have to adjust their positions very carefully And

Â it, and their weights are important as well, is because they are trying to sum

Â their torques to zero, and how they place themselves mat, matters.

Â If, for example, the riders are, have, essentially identical weights, and these

Â two riders do They need to sit at equal distances from the pivot because the

Â torque they produce, after all, is the product of the force they exert on the

Â seesaw times the lever arm they have to work with.

Â There's some subtleties in here with, with regard to the angles involved between the

Â lever arm and the force but In this situation we can really ignore those.

Â The forces and lever arms are essentially at right angles to each other, and our

Â lives are simple. So these two identical riders, seated at

Â identical distances from the pivot, produce identical but oppositely directed

Â torques, and the seesaw balances. What if we have a heavier rider around,

Â though? So instead of this rider, we bring up one.

Â And this is made of steel. This is heavy stuff.

Â So I'm going to put this rider in. If I put this rider out at the same

Â distance as the rider on your right It completely dominates, and I run the risk

Â of tossing this rider. This is one of the flaws with seesaws, is

Â it's easy for one of the riders to become an astronaut, when a very heavy rider gets

Â on the seesaw[NOISE] and does that to it. But this rider cannot sit that far out

Â from the pivot. Too much lever arm for a large force, and

Â therefore this rider dominates it, and produces a torque that, that one cannot

Â compensate With. Comp-, compensate for.

Â So I have to bring the heavier rider in close.

Â How close? Pretty close.

Â I'm almost at balance. There we are, this is balance.

Â Alright? It's as close as I'm going to get.

Â And, again, the net torque on the seesaw is zero, or pretty close to zero.

Â >> And, you'll notice that, that now the lever arm with which this rider is

Â producing the torque, is quite short because this one weighs a lot, so big

Â downward force, short lever arm. And that is balancing, or cancelling out

Â the torque due to this one, which is in the opposite direction, but it's produced

Â by a by a smaller force acting at a larger lever arm.

Â So this is common in, in playing on a seesaw when you have two children of, of

Â significantly different weights. They have to sit at different distances

Â from the pivot. The heavier child sits close to produce a

Â certain torque, and the lighter child sits far from the pivot to produce an equal

Â amount of torque but in the opposite direction.

Â Well, that brings us to a question. And the question is this.

Â Can two riders, and we can adjust their weights as you like.

Â Ever sit on the same side of the seesaw, and still balance the seesaw?

Â Two riders cannot sit on the same side of the seesaw, and expect the seesaw to

Â balance. That's because those two riders.

Â Produce torques in the same direction about the pivot.

Â Their forces are in the same direction, their lever arms are in the same

Â direction, so their torques are in the same direction.

Â And when you add those torques, they sum to something larger than each one

Â individually. So you get a lot of torque on the see-saw,

Â and its Terribly unbalanced. In order to balance the seesaw, the two

Â riders, or however many you want to put on the seesaw, have to distribute themselves

Â on opposite sides of the pivot so that their, their torques cancel one another

Â and eventually, if you do it all right, they sum to zero and the seesaw is

Â rotationally inertial. It has zero net torque on it and no angular

Â acceleration. It coasts rotationally.

Â There are two seemingly different ways to think about the balanced see saw

Â situation. The first way is the way we've been doing.

Â Where this rider produces a torque, that rider produces a torque, the two torques

Â sum to zero and as a result the seesaw experience zero torque due to gravity.

Â It's balanced. The second way to think about this

Â situation is in terms of a concept known as the center of gravity.

Â Now center of gravity is the effective location of an object's weight.

Â I have one. You have one.

Â These riders have one. Even the seesaw board has one.

Â This rider's center of gravity, that is where its effective weight is located.

Â Is pretty much at its center. Same with that rider.

Â The seesaw board's center of gravity, the location, the effective location of its

Â weight, is at its middle. Right there.

Â And that might make you think that center of gravity, which is here, and center of

Â mass, which is here, are the same idea. Center of mass, center of gravity, aren't

Â they the same? They're not.

Â They happen to coincide for all objects here near the earth's surface.

Â Celestial objects violate this concepts for complicated reasons that I'll leave

Â for another day. But small objects do have their centers of

Â gravity at the same locations as their center of mass, but they're different

Â concepts. Center of mass is the effective location

Â of an object's mass. It's natural pivot.

Â We watch centers of mass in action when I threw various wobbling objects or sticks

Â and so on through the air and you'd watch. The center of mass was f, traveling in the

Â arc of a falling object. That's the mass moving and the inertial

Â properties of the object In play. So, center of mass is all about intertia

Â in motion. Center of gravity is about forces and it's

Â forces of gravity. It's got to do with gravity.

Â If there's no gravity around, center of gravity means nothing.

Â So it's the effected location object's weight The fact that weight is

Â proportional to mass here near the earth's surface, means that center of gravity and

Â center of mass share the same location. But they're different concepts and so if

Â you're dealing with the inertial aspects of an object, you're probably paying

Â attention to the center of mass. Mass.

Â If you're dealing with the gravitational or weight aspect of an object, you're

Â probably dealing with center of gravity. So, back to the situation here.

Â We have objects with various centers of gravity and that brinks us to an

Â observation that this entire structure Two riders in a seesaw is, we can consider it

Â as a single object. Where is its center of gravity?

Â That composite object. And it turns out that this overall

Â object's center of gravity is located right above that Pivot.

Â And it's being pulled straight down, like the centers of gravity are pulled straight

Â down. They're gravity after all, right?

Â The forces of gravity are toward the center of the earth.

Â It's being pulled straight down right towards the pivot, the center of rotation.

Â And as we've seen before, forces that act toward the center of rotation produce no

Â torque about the center of rotation. So, this seesaw is balanced for two, you

Â know, in two ways you can think of it. One is in terms of the individual riders

Â producing torques that sum to zero. The other way, which is kind of cool, is

Â that the riders and seesaw together have a center of gravity located vertically above

Â the pivot. And therefore, the, the force of gravity

Â acting on this entire structure acts right toward the pivot, and produces no torque.

Â It's along the, the lever arm and produces no torque.

Â [LAUGH]So Annie and Megan here are riding a real seesaw, not one of the little

Â things I have in my lab. And They're balanced right now.

Â Can you show us this? It takes delicate adjustment, but Megan's

Â distance is just right from the pivot, the pivot's right here.

Â Andy's distance is just right from the pivot They've adjusted it, so the net

Â torque on this thing is, is as close to 0 basically, as they can get it.

Â But this is a boring way to ride seesaws, if you just sit here balancing.

Â I guess it's not too boring. It's kind of exciting, trying to keep it

Â balanced. But they can unbalance it In order to rock

Â back and forth in one of two ways. They can either push on the ground with

Â their feet. So, so Meagan, why don't you push on the

Â ground. Okay, and that extra force produces

Â another torque, which causes Annie to rotate down.

Â Now Annie can push down on the ground and cause Meagan to rotate down.

Â So, they're causing angular accelerations back and forth by exerting new torques on

Â it. The other way they can unbalance this Is

Â by leaning. So the, each, each one of them has a

Â center of gravity that's located somewhere sort of mid-body.

Â But if they lean, they can shift the location of their center of gravity and

Â therefore. Exactly where they're exerting the forces

Â on the seesaw board, and cause it again to experience a net torque so it undergoes

Â angular acceleration. So, if you both lean towards Annie, what

Â happens? >> It goes down[LAUGH] >> Annie goes down,

Â because basically the lever arm With which she's working gets longer.

Â And the one that Megan's working with gets shorter.

Â So the torque is this way, toward me. But how if we lean, everybody lean towards

Â Megan. >> [laugh] Now the lever arms get longer

Â and shorter in the opposite direction. Speaker:and then that torque is toward

Â you. So, they can rock back and forth, so, this

Â is how a seesaw works. Okay, you guys can go at it.

Â >> All right, here we go. Speaker:[unknown] Speaker:[LAUGH] Either

Â way. Speaker:[laugh] >> And this is what makes

Â seesaw fun right, is all the adjustments of the torque so that you[UNKNOWN] Undergo

Â angular acceleration in opposite directions, back and forth.

Â >> This is so funny! >> Seesaws are not the only structures in

Â our world that need to balance. Mobile sculptures do as well.

Â This mobile sculpture is entitled, happy hanging hardware.

Â And I built it out of a torque wrench, a ball peen hammer, and a metal file.

Â Amazingly enough, each of these components is rotationally inertial.

Â You don't see any of the them undergoing angular acceleration, after all.

Â And that brings us to a question. For all of the components of a mobile

Â structure, to be rotationally inertial, how must those components be arranged?

Â Each component of this mobile structure has its center of gravity at or below the

Â point at which that component is supported.

Â In effect, the pivot, about which that component could rotate.

Â This is actually a relatively complicated concept though.

Â Because there are three components here which aren't the individual tools.

Â First component, the, the simplest, is the, is the file That file has its center

Â or gravity at or below this support point. Which is the loop of string going around

Â it. That's the pivot about which the file can

Â rotate. And so, the file has its center or gravity

Â at or below that, that pivot. And therefore.

Â Gravity produces no torque on the file, it's rotational inertial.

Â So far, so good. The ball peen hammer isn't an object by

Â itself, it's not the component by itself. Rather, the ball peen hammer and the file

Â together are the next component of this mobile.

Â And that combined object. Ball peen hammer and file has its overall

Â center of gravity at or below its support point.

Â This loop of string. And lastly, the torque wrench and

Â everything below it has its combined center of gravity at or below this.

Â Support point. The support point that, that is acting on

Â the torque.wrench. So, each of these components, the file and

Â the hammer and file and the wrench, hammer and file, each of those components has

Â it's center of gravity directly below it's support.

Â And therefor, gravity and pulling down on the center of gravity produces no torque

Â on that component about it's pivot. It doesn't undergo any angular

Â acceleration then due to gravity, it's balanced.

Â And so the file is balanced. The hammer and file are balanced.

Â The wrench, hammer, and file are balanced. The entire mobile then, is balanced, and

Â it's all rotationally inertial. So we see that objects that can rock or

Â tip are only rotationally inertial if you balance them carefully.

Â Sometimes that's what you want, like with a mobile.

Â Sometimes that's almost what you want, like with a seesaw, where getting it

Â perfectly balanced is interesting, but kind of unexciting in the long run and you

Â want to unbalance it a little bit to get some action happening.

Â We'll talk more about balance in the episode on bicycles, but for now.

Â It's clear that in the context of seesaws, balance and near balance are the name of

Â the game.

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