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  • Hi. It’s Mr. Andersen and this AP Physics essentials video 54. It is on angular momentum.

  • Momentum remember is a product of the mass times the velocity of an object. So any object

  • moving with mass has momentum. The only difference in angular momentum is it is rotating or spinning

  • objects. And so if you were to try to get on this bicycle and balance without the kickstand

  • out you are probably going to fall over. But as you start to bike, as these wheels pick

  • up angular momentum, they are going to resist changes. And it makes it easier for you to

  • remain upright. And so angular momentum is a vector. So there is a clear direction in

  • which it acts. And in AP Physics you should be able to understand the angular momentum

  • of either a point object. So a point object is going to be an object accelerating around

  • a point. So it could be, for example, an object attached to a string or a planet orbiting

  • around the sun. And the equation is very simple. L is equal to our angular momentum. Again

  • it is a vector, which is equal to r, that is going to be the radius from the center

  • to the object. So that is the distance. Times its linear momentum, which would be the mass

  • times the velocity in a line. You also should be able to calculate the angular momentum

  • of an extended object. So the whole object is rotating around a point. So to figure that

  • out all we say is the angular momentum is equal to I, where that is rotational inertia,

  • times the angular velocity of the object. And again that inertia is going to change

  • depending on what that object is. Now to figure out the direction of this vector you will

  • use the right hand rule. So if we look at this one right here, the object is spinning

  • like that. So if you move your fingers in the direction of that spin, then we should

  • have angular momentum that is moving in the upward direction. Whereas on this one, since

  • it is rotating in the other direction, we are going to have it acting in the down direction.

  • Now we learned when we were dealing with impulse that if you apply a force for a given period

  • of time that is going to equal the change in momentum of the object. Well the same applies

  • here. So the change in angular momentum is equal to, not the impulse, but rather the

  • torque times the change in time. So that net torque times the change in time is going to

  • give us a change in that angular momentum. #00:02:15-5#

  • So angular momentum of this gyroscope, since we are spinning it in this plane, that is

  • going to keep it spinning in that plane and so it is able to resist changes due to gravity.

  • There are really neat things we will do in future videos. So you can take a wheel and

  • give it a certain amount of angular momentum like that, and so it is conserved but it can

  • be transferred, some of that angular momentum, as we change the angle at which that force

  • is actually acting. And so the two things you should be able to do in AP Physics is

  • calculate the angular momentum of a point object. Again that is an object that is moving

  • or rotating around a given point. So this could be an object attached to a string or

  • the moon orbiting around the earth. And so the formula is pretty easy. It is simply r,

  • which is the radial distance here, times the linear momentum. So linear momentum is going

  • to be in this direction. So it is the mass times the velocity. And so if you have these

  • three bits of information, the velocity of the object, the mass and the radius, all we

  • do is simply multiply those together. So let’s say we have an object, 1.1 kilogram mass traveling

  • at 3.2 meters per second. And then we have about 28 centimeter distance between the two.

  • All we are going to do is multiply those values out. And then we are going to get an angular

  • momentum of 0.99 kilogram meters squared per second. Now the one thing I should have included

  • here is that this is a vector value. So we have to add a direction to it. How do we figure

  • out the direction? Well since the rotation is like this, we use the right hand rule to

  • show that the angular momentum is going to be acting in the upward direction. You also

  • should be able to calculate the angular momentum of an extended object, like this rotating

  • cylinder here. All we do is multiply the rotational inertia times the angular velocity of that

  • object. So if it is given, let’s say we have an inertia of 15 kilogram meters squared.

  • We multiply that times our angular velocity, like that. And we are going to get 1.7 times

  • 10 to the second kilogram meters squared per second. Now this again is a vector. And so

  • what direction is that acting? Again, looking at my right hand rule it is going to be acting

  • in the upward direction. Now how do we measure this in a physics lab? A good way to play

  • around with this is using a turntable. So you can use a turntable that is attached to

  • a desk, has a certain amount of mass on it and what you can do is you can give it a spin.

  • So if we spin it in that direction, we try to make it as frictionless as we can. It is

  • just going to keep spinning in that direction. And these are generally pretty heavy. So they

  • have a large amount of rotational inertia. You can also attach a photo gate to it so

  • we could measure that angular velocity or the speed at which it is turning in radians

  • per second. And so you can do calculations of rotational inertia. We can also do collisions.

  • Let’s say we were to take another object, as the bottom object is spinning with a certain

  • angular velocity we could simply drop the top object on it. So what is going to happen

  • is the angular momentum is going to be conserved and so we are going to have to see a decrease

  • when we put both of these together in it its angular velocity. Also you should understand

  • how a change in torque or net torque over a given period of time is going to change

  • the angular momentum. This is just like impulse in regular translational motion. And so here

  • we have an object and we are going to apply a force to it in this direction. Remember

  • if we apply a force perpendicular to the lever arm we are going to get a torque. And so the

  • torque is going to be in this direction. So I am going to start the animation and watch

  • what happens to the angular momentum. So as I add a force in that direction we are getting

  • an angular momentum in this direction. What is causing that angular momentum? Again it

  • is the lever arm now times the momentum in that direction. So as we apply a torque it

  • takes awhile, but we are building up momentum in that direction. Now watch what happens

  • if we change the torque in the other direction. Again, it is already has some movement or

  • momentum in this direction. But now we have reversed the torque so it is going to be applying

  • a force in this direction. So the torque is down. Watch what happens. We are going to

  • see a decrease in angular momentum and then it goes in the other direction. And so again,

  • as we apply a torque against that angular momentum, what do we get? At this point we

  • can bring it to a stand still like that. So how could we model this? Well imagine we have

  • this turntable right here and I have rockets on either side. And they are going to apply

  • torque. So they are going to apply a force perpendicular to the lever arm, and as they

  • do that over time what is going to happen to the angular momentum? It is going to start

  • to speed up in that direction. Now how could you actually measure that without using rockets?

  • You could use a set-up like this. So we are using that turntable again. We could have

  • a little bit of a wheel down on the bottom where we can apply a force to it. And so I

  • am having an object go off the table. Now we can apply a constant force in this direction.

  • So that is going to be a torque over a given period of time. And that is going to give

  • me my change in angular momentum. So did you learn to predict the behavior of objects in

  • a collision as they conserve angular momentum? Could you calculate the angular momentum of

  • both a point object and an extended object? And also could you use torques and changing

  • torques to see how that impacts the angular momentum of the object? I hope so.

  • And I hope that was helpful.

Hi. It’s Mr. Andersen and this AP Physics essentials video 54. It is on angular momentum.

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角運動量 (Angular Momentum)

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    Cheng-Hong Liu に公開 2021 年 01 月 14 日
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