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.