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 does a lone seesaw ride plummet to the ground?

Â The answer to that question is that the lone rider produces a torque on the seesaw

Â and causes it to undergo angular acceleration.

Â The seesaw rotates such that the rider descends toward the ground.

Â And hits it. There are several ways of examining this

Â situation. So I'm going to follow the path that I

Â think is most straightforward. The rider's weight gives rise to a torque

Â on the seesaw. And since the seesaw is no longer

Â rotationally inertial, its angular velocity is no longer constant.

Â Instead, that angular velocity changes with time, and the rider soon plummets to

Â the ground. But those observations give rise to two

Â more questions. How does the seesaw respond to torques,

Â and what is the origin of this particular torque?

Â So let me start by looking at the seesaws response to torques.

Â When the seesaw is experiencing no outside torques it's covered by Newton's first law

Â of rotational motion. So it rotates at constant angular

Â velocity, like this. But once there is a torque acting on the

Â seesaw, the seesaw is no longer covered by angu-, by Newton's First Law of Rotational

Â Motion. And its angular velocity is no longer

Â constant. Instead, it's angular velocity begins to

Â change with time. The seesaw undergoes angular acceleration.

Â Angular acceleration is another vector physical quantity of rotational motion,

Â and it is the rate at which angular velocity is changing with time.

Â Like ordinary acceleration, translational acceleration, it's a subtle quantity.

Â It's hard to see. You have to look carefully.

Â It takes three glances. To see acceleration and it takes three

Â glances to see angle acceleration. So I'm going to illustrate angle

Â acceleration with my body and hope that you can see.

Â It happening. So here we go, let me start, motionless,

Â rotationally motionless. That is my angle velocity is 0.

Â If I change my angular velocity, during the time over which that angular

Â velocity's changing, I am undergoing angular acceleration.

Â So here we go. I'm going to g-, undergo angular

Â acceleration, and then I'm going to stop undergoing angular acceleration, and watch

Â what happens. Here goes the angular acceleration; it's

Â going to be... (End of transcription.) Up.

Â Right hand rule again. I'm going to rotate.

Â Here we go. Shoop.

Â Okay, I did it. It;s over.

Â I am now coasting rotationally, at constant angular velocity.

Â But when I first got started I was undergoing angular acceleration.

Â If I don't go, undergo angular acceleration again, I'm going to keep

Â spinning here forever, and this will make me very dizzy.

Â So I'm going to undergo angular acceleration downward in a moment.

Â Ready? Get set, whoop, there I did it.

Â So during those two moments when I changed, extended moments.

Â When I changed my angular velocity I did it by way of angular acceleration.

Â I'll show it to you again. I'm going to do A intersection upward for

Â about a quarter of a second and then, I'm going to do A intersection downward for

Â about a quarter of a second and come to stop.

Â Ready? There.

Â Now, I'm coasting and now. So, the angular acceleration portion of

Â that situation Was during the changes in my angular velocity.

Â Coming back to the seesaw then, the angular acceleration is absent now.

Â Ready, get set, there it is. There were a lot of angualar accelerations

Â there at the bottom, but they initially kicked in, the first angular accelerations

Â Kicked in when the rider got on the seesaw.

Â Right now. So we see, a torque causes a seesaw to

Â undergo an angular acceleration. But what if there's more than one torque,

Â acting on that seesaw at the same time? In that case, those torques add together.

Â To be come a net torque, and the net torque is what causes the angular

Â acceleration. So for example if I've got 2 riders

Â hopping on to the seesaw at once, the seesaw can't respond with several separate

Â angular accelerations at the same time, it, it only has 1.

Â Instead it responds to the net torque, produced by those 2 riders.

Â Well, if net torque causes angular acceleration, the question comes up is,

Â how much angular acceleration? It turns out that the seesaw's angular

Â acceleration is proportional to the net torque acting on it.

Â So if a gently net torque acts on a seesaw.

Â It undergoes a small angular acceleration. But if a large net torque acts on the

Â seesaw,[SOUND] it undergoes a large angular acceleration.

Â But there's a second factor involved in determining the seesaw's angular

Â acceleration, the seesaw's rotational mass.

Â Rotational mass is the measure of an object's rotational inertia, its

Â resistance to undergoing angular acceleration.

Â Now traditionally that physical quantity is called moment of inertia and it has

Â various complexities to it. They're beyond the, the scope of our

Â little discussion here. Not relevant really to seesaws.

Â So rather than trying to have you remember a name like moment of inertia, with its

Â complexities, I'll make our lives simpler by simply calling it.

Â Rotational mass. That conveys the characteristic that it's

Â a mass like thing, it's a resistance to acceleration of some form.

Â In this case, rotational acceleration. So, this seesaw has a certain rotational

Â mass, a certain resistance to angular acceleration.

Â So if I exert a certain torque on it. It responds with a specific angular

Â acceleration. And I go back to, to putting a rider.

Â So, my little rubber stopper rider is here.

Â If I put a certain rider on this seesaw and let it undergo angular acceleration,

Â well, it undergoes rather rapid angular acceleration, and down goes the rider.

Â But I can increase the rotational mass of this seesaw.

Â By adding a second board. When I do this, I'm increasing the

Â rotational inertia of the seesaw. Try to glue it and tape it in place.

Â And now, it's less responsive to the same torques as before.

Â In this case, if I put 1 rider on. It undergoes angular acceleration, but not

Â as much. Overall, the seesaw's angular acceleration

Â is proportional to the net torque acting on the seesaw.

Â And also inversely proportional to the seesaw's rotational mass.

Â Those two observations form the basis. For Newton's Second Law of Rotational

Â Motion, which states that an object's angular acceleration is equal to the net

Â torque acting on that object divided by that object's rotational mass.

Â I'm going to ask a question about angular acceleration, but I'm going to do it in

Â the context of a bicycle wheel that I can hold in my hands.

Â At present the bicycle wheel is motionless.

Â And I'm going to do three things to it, in sequence.

Â First, I'm going to start it spinning. Second, I'm going to turn the wheel all

Â the way around like this, so it's spinning in the opposite direction.

Â And now as a third thing, I'm going to stop it from spinning.

Â The question is, during which of those 3 steps was the bicycle wheel undergoing non

Â zero angular acceleration? All three steps involved angular

Â acceleration of the wheel. When I started it spinning it went from

Â having an angullar velocity of zero to having an angular velocity toward you.

Â Remember the right hand rule here. When I pivoted it.

Â Around like this. I reverse the direction of the wheels

Â angular velocity from toward you to toward me.

Â That's angular acceleration. I had to, to make the wheel undergo

Â angular acceleration to reverse its direction of, of rotation.

Â And finally, when I stop the wheel from spinning, I take its angular velocity from

Â >> Toward me to zero. So, all three steps require the wheel to

Â undergo angular acceleration. So, we see that a seesaw responds to a net

Â torque by undergoing angular acceleration. Why then does a low rider sitting at the

Â end of the seesaw board. Exert a torque on that board.

Â After all, the rider has a weight, which is a force.

Â And If I hold the seesaw in place now, the rider and seesaw are pushing on each other

Â with forces. The seesaw to support the rider's weight

Â and the rider pushing back on the seesaw in response.

Â It's all forces out here. Where does the torque come from?

Â Well it turns out that forces and torques are related and that a force can produce a

Â torque and a torque can produce a force. To see how that all works, let's go

Â experiment with a door. ...because doors are a wonderful example

Â of rotational motion and the use of a force to produce a torque.

Â So here I am outside the physics building, opening and closing doors in a light rain.

Â The things we do for science. Doors are a nice example of rotational

Â motion. After all, they don't go anywhere.

Â They simply rotate open and closed about their hinges.

Â (End of transcription.) >> They have all of the characteristics we've come to

Â expect of rotating objects. They have angular postions, they have

Â angular velocities, and they even have angular accelerations.

Â But that brings us to the issue at hand, which is when you open a door you do it by

Â exerting a force on the door handle. And yet the door undergoes angular

Â acceleration. Well, angular accelerations are produces

Â by torques, not by forces. So how is it that a force exerted on the

Â door handle produces a torque On the door. To show you how that works, I first have

Â to define a center of rotation. Now, the obvious place to put the center

Â of rotation is somewhere along the hinge line.

Â 'Because that's the line about which all the ro-, door's rotation occurs.

Â But I have to be more specific than that. Because center of rotation is act-.

Â Actually a point. Not a line.

Â So I'm going to put the center of rotation in line horizontally with the door handle

Â for reasons that we'll come to eventually. And that's going to be our center rotation

Â right there on the hinge line aligned nicely with the door handle.

Â Having done that then, let's look at ways in which not to produce a torque about

Â that center rotation. Starting with a force, so these are all the unsuccessful ways to

Â try to open a door, some of which you may have encountered by accident.

Â So, first unsuccessful way to produce a torque, starting the force, is to push the

Â door handle toward. The center of rotation.

Â So I'm pushing right at that center of rotation.

Â No effect. I'm producing no torque.

Â How about reversing my force? Instead of pushing toward the center of

Â rotation, let me pull away from the center of rotation.

Â Also, no luck. Doesn't do anything.

Â So we see that. Pushing toward or away from the center of

Â rotation is, is unsuccessful. How about pushing on the center of

Â rotation. Let me come over here to the center of

Â rotation and push right on it. I'll try to pull right on it, all the kids

Â of forces, none of it works. So you can't move the door by exerting

Â your force toward, away from or on the center of rotation.

Â Okay. Now it's time to be successful.

Â We can only take so much frustration. So now, I'm going to exert a force out

Â here on the door handle, not toward or away from the center of rotation, but at

Â right angles to a special line. It's actually a vector.

Â It's called the lever arm. And this is the, this is what the lever

Â arm is. The lever arm is going to be the vector

Â that, that extends from the center of rotation to the point at which I'm going

Â to exert my force. Namely on the door handle.

Â So there is a vector that points along this lineto this point here.

Â It has a length of about 1 meter like that and it's direction is exactly to your

Â left. And I'm going to exert my force Not along

Â that vector or, you know, with it or against it, but at right angles to it,

Â perpendicular to that lever arm. I'm going to exert my force toward you,

Â and watch what happens. The door undergoes angular acceleration

Â and begins to rotate open. That is how to produce a torque starting

Â with a force. If you'll exert your force At a lever arm.

Â From the center rotation, that is the vector that extends from a center of

Â rotation to where you exert your force. And you exert your force at perpendicular

Â to that lever arm. Then you produce a torque.

Â And the torque has a specific direction. Its direction follows yet another right

Â hand rule. If you take your right hand and extend

Â your index finger. In the direction of the lever arm towards

Â your left right now. And then you swepp the index finger of

Â your right hand in the direction of the force which is towards you.

Â So that's the sweep. Look what my thumb is doing.

Â My thumb is pointing up. That is the direction of the torque I

Â produced in pulling toward you. With, on the door handle.

Â The lever arm is that, that direction. The force is toward you.

Â The, the torque I exert is up, and so it causes upward angular acceleration in the

Â door which swings open. Now the amount of that torque that I

Â produce depends on two things. One is how much force I exert.

Â The torque is proportional to the force I exert.

Â A gentle force produces a gentle torque. A big force produces a big torque.

Â So, that's the first observation. Second observation is, the length of the

Â lever arm matters. The torque I produce is proportional to

Â the length of that lever arm. Here I have a lever arm about that long,

Â but if I go inside and I push near the hinges, I can make the lever arm very

Â short; and watch what happens. That was hard.

Â So, I'm exerting my force here, very close to the pivot, Pivot.

Â Therefore at a very short lever arm, and I'm obtaining a very small torque until I

Â really crank up my force. We can combine these observations to

Â relate the force to the torque it produces, quantitatively.

Â That torque is equal to the lever arm times the force.

Â Where only the component of force that is perpendicular to the lever arm is

Â included. And where the torque is in the direction

Â determined by the right hand rule. So in this case if the lever arm is

Â pointing to your left and the force is pointing toward you The torque is up.

Â Now this door is complicated because it has a closing mechanism, like many doors.

Â It has a system to try and keep that door closed when you leave it alone.

Â So it's not free to exhibit rotational inertia and has all kinds of, of its own

Â trouble and I had to overcome that resistance, That, that The mechanism

Â trying to keep the door closed. That's a lot easier to overcome if I'm out

Â here at a, with a big lever arm. I can exert relatively gentle force on the

Â door handle and get the door to open despite the closing mechanism.

Â If I try to push very close to the hinges, that closing mechanism is hard to beat.

Â And you may have had this experience that if you go to a door that isn't very well

Â labeled and you have to push it open, you can't tell which side of the door has the

Â hinges. If you push near the hinge side of the

Â door, the door doesn't open very easily. It's very resistant to openeing because

Â you're producing so little torque with your force.

Â You need to go out to the other side of the door where you have a big lever arm to

Â work with. And therefore can really create a lot of

Â torque with a small force. To produce a torque with a force then, all

Â we need is a lever arm. For an unconstrained seesaw like this.

Â One that can rotate in any possible direction, the options are limitless.

Â I'm going to choose as our center rotation The seesaw's center of mass just for

Â convenience here, right about there. And now, let me show you a couple of

Â torques. Things you've seen before, maybe some you

Â haven't. If I come out here to a lever arm Towards

Â your left and then I push down with my force, which is at right angles to that

Â lever arm or, in fact I don't have to be perfectly right angles I have to just,

Â just have to have some component that's at right angles to the lever arm.

Â And I push down, I cause an angular acceleration toward you.

Â Right hand rule again. On the other hand, if I come out to a

Â lever arm, same lever arm. But I push my force towards you.

Â Watch what happens. I cause angular acceleration up.

Â And if I come out to a level arm toward you, very short one but it's there, and

Â push down, I caused angular acceleration to your right.

Â I flipped the board like that. Well.

Â This is exciting, but very complicated. There are too many options with our

Â unconstrained seesaw. So fortunately, we're going to focus on a

Â constrained seesaw, one that has a pivot shot through the center that forces it to,

Â to rotate in a very simple manner. >> This seesaw board down here cannot do

Â this kind of rotation, or this kind of rotation.

Â And so, it operates in a more simple fashion, like this.

Â And it still exhibits the same sorts of behaviors.

Â To produce a torque on this seesaw, I come out to a lever arm and push at right

Â angles, or partly at right angles to that lever arm down and I cause angular

Â acceleration toward you. Because my torque was toward you.

Â We've seen how to produce torques with forces in the context of doors, in the

Â context of seesaws. But what about another important household

Â use of torques, putting in or taking out screws or bolts?

Â You rotate a bolt into place and you rotate it the other direction to take it

Â out of place. Well suppose you have a big bolt like

Â this. >> That has rusted in place, and you're

Â trying to get it out but it won't turn when you grab it with your hand and try to

Â twist. You need more torque.

Â So, in that case you get a wrench. This is a device, and you will have to

Â figure out how it works. This is a device that when you put it on

Â the head of the, the bolt. >> It allows you to produce more torque.

Â And by now, you should be thinking about how this works.

Â But what if this is really, really stuck? And you need a bigger wrench?

Â Well, that's already a pretty big wrench, you think.

Â And you're probably thinking that I'm going to go over and get this wrench.

Â To show you the bigger wrench. But no.

Â I have in mind this wrench. And so we take this wrench, put it on our

Â stuck bolt. And lo and behold, it's a lot easier.

Â To produce a large torque on that bolt and remove it from wherever it's stuck.

Â The question then, is this, why is using this larger wrench more effective it, why

Â does it enable you to remove that bolt when this wrench didn't to the job?

Â This wrench has a longer handle, and it provides a longer lever arm with which to

Â produce a torque using a force. So when you come out here to the end of

Â the handle and push perpendicular to that handle and therefore perpendicular to the

Â lever arm. Your force produces a larger torque as

Â compared to this wrench. There's just not as much length here to

Â work with. It's got a shorter lever arm and so when

Â you push on the handle of this wrench with that shorter lever arm your force produces

Â less torque. So we see, whenever a lone rider goes out

Â to a lever arm on the seesaw and sits down, the rider's weight gives rise to a

Â torque on the seesaw that causes it to undergo angular acceleration, such that

Â the rider ends up pretty much sitting on the ground.

Â The rider's weight. Is a force and that weight causes the

Â rider to push on the seesaw with a force, but the force acting at a lever arm from

Â the center rotation produces the torque that causes all this to happen.

Â Pretty much the only place a, a single low rider can, can sit or stand and not

Â produce a torque. On the seesaw is exactly on top of the

Â pivot, which is kind of an interesting place to stand.

Â And I must admit to having done that myself, from time to time.

Â But it's much more fun to have 2 riders on a seesaw, and that is the subject for the

Â next video.

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