Hi. It’s Mr. Andersen and this is AP Physics essentials video 69. It is on angular impulse.
Remember an impulse in physics is a force applied for a given period of time. Well then
what is an angular impulse? It is when you are applying a force to a rotating system.
Then what you are doing is applying a torque to that system. And so a good example of that
is playing tether ball. When you hit the ball in tether ball and what you are doing is applying
a force perpendicular to the rope which comes from the center of that rotating system. So
if we look at it from above, when you apply a force in this direction, so that is a torque,
what you are doing is applying a force for a given period of time. And that torque causes
a change in the angular momentum. It keeps spinning until eventually we get a force exerted
by the pole when it gets to the center. And so if you have a rotating system like this,
as long as it has angular velocity then it is going to have angular momentum. Now let’s
say we apply a torque, so we apply a force to it for a given period of time. So if we
draw in our force applied to that system, what is going to happen to the angular velocity
and therefore the angular momentum of the system? Well it is going to increase. We could
figure out the direction using the right hand rule. But that change in momentum is equal
to the torque times the amount of time that we are applying it for. And so that is going
to be the angular impulse. If we know what that torque is we know how much time it is
going to be applied for we immediately know what is that change in angular momentum. Now
it is important that we understand the difference between translational and rotational motion.
And so if I apply a force right to the center of mass like that it is just moving in that
direction. So I have accelerated that object. And like I have showed you in the impulse
video, if force is equal to mass times acceleration, if we say acceleration is the change in velocity
over time and then we simply multiply both sides times time, we now have momentum change
on the right and we have impulse on the left. But this would be for a translational system,
where all of the motion is in one direction. That change in p or the change in momentum
is the impulse. Now if we look at a rotating system like this, where I apply a force like
that, it is rotating, let’s get to our equations there. We now have a torque and that torque
is equal to the rotational inertia, instead of mass, times the angular acceleration, instead
of the acceleration. Now we could get that angular acceleration and break that out. That
is going to be the change in angular velocity over time. Multiply both sides times time
again. And what do we get? Change in angular momentum on the right. And what do we have
on the left? This is going to be our angular impulse, or delta L. And so let me give you
a specific problem. Let’s say we have a motor cross person. They are going off of
a jump and they are applying a force up. And that is causing them to do a flip like that.
So, if we solve a problem where we know what the force is, let’s say it is a 25 newton
force in this direction, and we know the distance from that center of rotation, let’s say
it is 1.9 meters, and we know the amount of time that we are applying that force, let’s
say it is 0.53 seconds, we can solve the change in angular momentum. So change in angular
momentum is simply equal to the torque times the change in time. Now what is our torque?
Torque remember is going to be the product of the force times that radial distance. And
so it is going to be force times radial distance times the change in time. So if I just plug
in these values up here, what do we get? 25 newtons times 1.9 newton distance from the
center. And them times 0.53 seconds. I get a change in angular momentum of this, solving
for significant digits, I get 2.5 times 10 to the third newton meter seconds. That is
going to be change in angular momentum. What would happen if we applied a greater force?
We are going to have a greater change in angular momentum. What if we applied it for a longer
period of time? We are going to have a greater change in angular momentum. Now how could
you test this in the laboratory and make sure that this equation worked? Well it would be
nice if we had a large spinning disc. We could apply a force on one side, maybe a rocket.
So we could apply a torque to it for a given period of time and watch its change in angular
momentum. It is difficult to do that. But we could have a set up like this, where we
have a large disc. And then we apply a force to it. So we are going to apply a perpendicular
force, so a torque to it for a given period of time. And we could use photo gates to measure
its change in angular momentum. And so did you learn to use appropriate mathematics to
figure out angular impulse change in angular momentum? And then finally could you test
the relationship between torque, time and change in angular momentum? I hope so. And
I hope that was helpful.