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.