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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.

# 角動量 (Angular Momentum)

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Cheng-Hong Liu 發佈於 2021 年 01 月 14 日