Anderson Video - Angular Momentum Vector

Professor Anderson
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>> Hello class, Professor Anderson here. We're talking about angular momentum. We just talked about this idea of the cross product. Let's see if we can apply angular momentum to a particular problem. So let's look at the ball on a string problem. And let's calculate what the angular momentum is for that particular ball on a string. So let's see what the problem looks like. We've got a ball on a string that is going to move around in a circle. And we will look at a particular top view, ok. And this thing is moving around at some particular speed, v. Ok it has some mass, m. And it's out here at a radius, r. Let's see if we can calculate the angular momentum for this very simple problem. What we said earlier was L was equal to r, oops, L was equal to r cross p. Ok but we know exactly what p is, p is just mv. And since m is a constant that can come right out in front and we just get m times r cross v. Ok that's what the angular momentum is. And now we have to worry about two things, what direction is r? What direction is v? So if we think about this particular point we have an r going out from the axis of rotation to the object of interest. We also have a v at that particular time that is at a right angle to r, ok. So with those few things let's see if we can calculate what r cross v is. R cross v, according to our definition for the cross product, this is just r times v times the sine of the angle between them times n hat, this direction that we have to find from the right hand rule. But the angle between them we just said was 90 degrees so this becomes rv sine of 90 degrees n hat sine of 90 is just 1 and so we have rv n hat. Alright now we need to figure out the direction for this thing. So to figure out the direction for the right hand rule we said fingers straight in the direction of r, ok, fingers straight in the direction of r. Curl your fingers towards v, curl them up towards v and what you should get is something coming out of the page right towards you, ok. And the way we draw something coming out of the page right towards you is with an x, right? Nope, that's the other one. A dot, right? Which ones the x and which ones the dot? Well I think of it like an arrow, ok. If an arrow is coming right at you that's got to be a dot because you see the point of the arrow. If the arrow is going away from you then it's an x because you're seeing the feathers. So we want something that's coming out of the screen towards you guys and that means I need a dot and so this is a direction of the angular momentum, ok. Now it has a magnitude given by that. And so we can put it all together now to calculate l for this ball on the string. L is equal to m, time to change the order just slightly, times v times r, n, the direction is out of the screen, ok, that's the angular momentum for a particle on the string.
>> Hello class, Professor Anderson here. We're talking about angular momentum. We just talked about this idea of the cross product. Let's see if we can apply angular momentum to a particular problem. So let's look at the ball on a string problem. And let's calculate what the angular momentum is for that particular ball on a string. So let's see what the problem looks like. We've got a ball on a string that is going to move around in a circle. And we will look at a particular top view, ok. And this thing is moving around at some particular speed, v. Ok it has some mass, m. And it's out here at a radius, r. Let's see if we can calculate the angular momentum for this very simple problem. What we said earlier was L was equal to r, oops, L was equal to r cross p. Ok but we know exactly what p is, p is just mv. And since m is a constant that can come right out in front and we just get m times r cross v. Ok that's what the angular momentum is. And now we have to worry about two things, what direction is r? What direction is v? So if we think about this particular point we have an r going out from the axis of rotation to the object of interest. We also have a v at that particular time that is at a right angle to r, ok. So with those few things let's see if we can calculate what r cross v is. R cross v, according to our definition for the cross product, this is just r times v times the sine of the angle between them times n hat, this direction that we have to find from the right hand rule. But the angle between them we just said was 90 degrees so this becomes rv sine of 90 degrees n hat sine of 90 is just 1 and so we have rv n hat. Alright now we need to figure out the direction for this thing. So to figure out the direction for the right hand rule we said fingers straight in the direction of r, ok, fingers straight in the direction of r. Curl your fingers towards v, curl them up towards v and what you should get is something coming out of the page right towards you, ok. And the way we draw something coming out of the page right towards you is with an x, right? Nope, that's the other one. A dot, right? Which ones the x and which ones the dot? Well I think of it like an arrow, ok. If an arrow is coming right at you that's got to be a dot because you see the point of the arrow. If the arrow is going away from you then it's an x because you're seeing the feathers. So we want something that's coming out of the screen towards you guys and that means I need a dot and so this is a direction of the angular momentum, ok. Now it has a magnitude given by that. And so we can put it all together now to calculate l for this ball on the string. L is equal to m, time to change the order just slightly, times v times r, n, the direction is out of the screen, ok, that's the angular momentum for a particle on the string.