Hi. It’s Mr. Andersen and this is AP Physics essentials video 68. It is on the angular
momentum of a system. Now if you give a top rotation it is going to start to pick up angular
momentum. You just remember, using the right hand rule you can put your finger in the direction
of the rotation and it is going to have rotational momentum perpendicular to that. Now if you
notice a top as it spins, it is starting to pick up this wobble. We call it the precession
in physics. And it is going to get bigger and bigger and bigger. And eventually that
top is going to come to a stand still. And the reason why is that there is not just one
angular momentum acting on that top. And so if we look at it, it is rotating in this direction.
So it would have the angular momentum in this direction. But there is another force, therefore
another torque acting on the top. That is going to be the force due to gravity. And
it is acting in this direction. So again using the right hand rule, we are going to have
a force coming right at us. And that is causing this precession up here, or this wobbling
of the top. Our earth experiences the same thing. So it is rotating but as it rotates
it is going to slowly do this big wobble. Now it takes 26,000 years for it to do that
wobble. And it is not a top, so it is not sitting on a table, so there can not be a
force of gravity acting on it. But there are other objects, like the sun, the moon and
even other planets that are tugging on that, applying a force to it and that is why it
is getting this precession. And so if a system has objects inside it that are in motion,
it is going to have angular momentum. And to figure out the angular momentum of the
entire system, all you have to do is figure out the angular momentum of all of the objects
inside that system. Now those could be point objects, like a ball revolving around a string.
To figure out the angular momentum of that, remember all you do is take the radius or
the distance from the center to the object and then you multiply that times the individual
momentum of that object. In other words its mass times its velocity. If it is an extended
object like this, to figure out its angular momentum all you do is multiply its rotational
inertia times its angular velocity. And so if we have a system like a helicopter and
that blade on the top is rotating, as it rotates we are going to have angular momentum. Now
the angular momentum in this case would be pointed up. Now what is going to happen to
that helicopter if we only have one blade on it, as it exerts a force on the air the
force is exerting a force back on it and so the bottom part of the helicopter is going
to start to rotate as well and be out of control. And so what they do is add another object
to the system. You have a tail rotor and that tail rotor as it spins is applying another
angular momentum and so we can use that to keep our helicopter stable. Now to calculate
the angular momentum of a point object all you do is take an object that is revolving
around a center. And you are going to multiply the radius times the momentum of that object.
And so the momentum of the object remember is going to be the mass times the linear velocity
of that object. And we simply multiply it times the radius or the distance from the
middle. Now in which direction is that angular momentum? We use the right hand rule. And
so as I move my hand in the direction of the object we are going to have angular momentum
that is going to be pointed up. If we are looking at an extended object like this, all
we do is multiply the rotational inertia times the angular velocity. In other words, how
fast it is spinning. Now in which direction is that angular momentum acting? As I move
my fingers around it is going to be acted in the up direction on that extended spinning
object. Now a great way to study this is using a gyroscope. And so this is a video from MIT.
There is a longer video description of this. I will put it down below but I am getting
kind of to the highlights of it. And so what they have done is taken a gyroscope. They
have spun it up. It has a huge amount of mass therefore a huge amount of rotational inertia.
And so it is spinning. You can see the direction of spin right here. And so as it spins in
that direction what they are going to do is they are going to apply a force, so they are
going to apply another momentum on the other side of it. Or a torque on one side of it.
And so you have to try to figure out what is going to happen to that gyroscope as it
does it. And so as I use my right hand rule of the gyroscope itself, what we are going
to get is there is going to be angular momentum pointed out in this direction. And so what
they are doing is adding another force. So they are going to add angular momentum to
it. And so they are going to add a force in this direction. And so to figure out which
direction that is going to go, you have to use your right hand rule as well. And so what
I am going to do, again it is centered on this point and they are applying a force in
that direction, so I am kind of moving my hand like this, and what should happen is
there should be a force towards me. And so as I let this go you can see that as they
push up it actually turns in a non-intuitive direction. It is moving in a direction that
really does not make sense unless you understand that this is an entire system. And that entire
system is made up of the angular momentum of all the objects. Now you try. So now it
is spun up again and what they are going to do is point down. And so try to use your right
hand rule to figure out what is going to happen to that gyroscope. And now let me play it.
And so you should have predicted, since you were pushing down on it there is going to
be an angular momentum that is pointed away from you. And so it is going to move in that
direction. Now it really takes that right hand and figuring out where you are in relation.
So again we are doing the same thing now. So this time we are pointed towards us. We
are applying a force towards you. And so what is going to happen to that gyroscope? Try
to figure out what is going to happen to it? I think I know what is going to happen to
it. So they are pushing towards us. And it is actually moving down. So again, it does
not make sense unless you really can stick to that right hand rule and figure out what
is going on. And then if we were to do one more, so we are going to set that up. So now
it is going to point away from us. And so I think I have it figured out. As they push
away from us it is actually going to move up. And so again, what is the angular momentum
of a system? It is the angular momentum of all of the objects within that system. And
so could you describe a model, again a gyroscope is a really good one. So you could analyze
what happens when we add multiple objects to a system? I hope so, and I hope that was helpful.