in this video we're going to be talking about angular momentum how it's conserved as well as angular impulse I put this web comic here by XKCD so this is Randall Monroe who did this he's so clever so I was like that what are you doing I'm spinning counterclockwise each turn robs the planet of angular momentum slowing it spin the tiniest bit and lengthening the night and pushing back the dawn giving me a little bit more time here with you isn't that sweet so let's remind ourselves what we do here so do you remember the equation for linear momentum just palal MV well remember now in uh rotational terms we have an equivalent here so instead of momentum like linear momentum we have angular momentum which is L so we're going to say l equals and remember the rotational equivalent of mass is actually moment of inertia and the rotational equivalent of velocity here is actually angular velocity Omega so really we have this equation just Lal I Omega okay so I just want to point out remember that the angular momentum is a the rotational equivalent of P right so angular momentum and we can call this L right so here we go and let's look at the units for things so let's do angular velocity first that's in radians per second all right then we've got um moment of our ner to remember the equation for I goes uh Sigma Mr R 2 so that must be kilog time distance squar so me squared now if we put this together then if we want to figure out the units for angular momentum we'll just multiply the units for I * Omega so in other words kilog s radians per second however we often omit the radians we often just you know ignore it so we're going to say it's kilogram me squared that's just a unit for moment of inertia we're going to say per second so there we go it'll be like this instead so there we go there's our equation now what's interesting though is that it's often conserved so the total angular momentum maybe I'll put this down here this is an important piece of information here the total angular momentum is constant as long as there are no external net torqus acting on it because remember that makes it accelerate so remember our equation goes L equals I Omega and you remember that I contains m r 2 so it's like L equals some kind of well some kind of Mr 2 because that's what I is time Omega okay because this is what I is the reason I put this down like this is I want us to concentrate on two things here I want us to concentrate on R and Omega that if R gets bigger if this thing is in a constant motion okay so total angular momentum is constant as long as there's no external net torqus acting on it then what happens well then this this value of L Remains the Same so how can we use this well you can use this for a fig a spinning figure skater so someone who's spinning for example they have a radius of their arms right so their arms are out at some certain R here and what happens then if they want to spin faster what should they do they should take their arms and make them smaller so bring their arms in as they rotating okay so as they're spinning around okay you can see me spinning around here as I'm spinning around if I brought my arms in what would that do well assuming there's no external net torqu then that means as long as my mass stayed constant which I'm assuming it did in this case if R gets smaller what happens to Omega Omega has to get bigger in order to keep L the same so if R goes down Omega goes up if R goes up Omega goes down so this right here let me just show you a uh video I think I have something actually repaired here so let's take a look so just take a look at this right here you see so uh she's spinning around as she brings in her arms she made her r value smaller that means Omega got bigger and by the way to slow down what do you do bring your arms out again so when she wants to actually stop spinning she puts her arms out do you notice that by putting her arms out that made all the difference isn't that kind of cool now um this happens in really large things as well so this is a neat story but um in the year 1054 in China um some people so they they were looking up at the stars and they saw hey look at that there's a new moon out there so it was actually brighter than the moon so they looked at this and they're really good at mapping where things were that's how we know it was in 1054 and they you know they saw this big bright thing it lasted some days and after that it went down again and they couldn't see it anymore what's interesting about it is if we know where to look because the Chinese were so good at mapping out where it was we can look now with our telescopes and see and this is what we see it's this thing here called The Crab Nebula now it looks like a big cloud of uh dust and gases isn't it beautiful this is really what it looks like and it's actually in 3D so it's hard to imagine but this is basically we're seeing the outer parts and the inner parts we can actually sort of see into it but the reason I mentioned it here is because hey in astronomy if our theories were correct we thought hey you know what we think this happened because the Chinese saw a black um not a black hole a supernova so if there was a supernova explosion which is when a star collapses on its own basically bounces off a solid Neutron core and then you know all the material gets just sent out Ward so it's sort of an implosion that turns into an explosion um if that happened you know our theories went that hey there should be a thing called a neutron star that's in the center and that thing in the center then we figured hey you know what it should be we scientists figured you know it there should be a neutron star and we should be able to find it what's beautiful about it you can if you look at the right place you look right in the center of it there is a neutron star that's spinning now interestingly enough this is just the remnant of a giant super super massive star so imagine this big big star it used to be really big but after it blew up of course a lot of pieces went missing yes of course but a lot of it also got collapsed and contracted and made more dense so imagine that this is our situation right where we have constant angular momentum and then what do we do the star itself other than the stuff that blew off a lot of it actually got collapsed and compressed so that stuff remember it took its radius and made it a lot smaller what what happens then well that means if you take a something that's way way bigger than our sun and you collapse it to the size of a city which is about you know about the size of a neutron star so this one here if you collapse it to the size of a city what do you think that does to Omega Omega goes way up doesn't it so when a star normally rotates quite slowly turns out we look at the center of this particular one in the Crab Nebula and we did we found a neutron star and we expected it to be spinning pretty fast right it actually spins the one at the center of the Crab Nebula spins 30 times per second it's called a pulsar cuz it actually the way we're lined up is like a pulse of light that sort of hits us it's cool isn't it so spinning uh figure skaters has to do with spinning neutron stars in The Crab Nebula for example after a supernova explosion how awesome all right so let's look at this we've got something called angular impulse as well remember the equation that we had for regular impulse so for linear impulse we had this quantity J which was equal to the um well we write f * delta T which is equal to Delta P so this is the force times the change in time which is also equal to the change in momentum well we have an equivalent for angular impulse as well so remember that P for example is just equal to MV in linear terms at least so we can say it's Delta this so what do we do then for our rotational equivalence well J is going to be called Delta l that's going to be the angular impulse now what's the equation going to be well let's see we have F so what's the angular equivalent kind of well it's torque we still have a change in time so it's delta T and if we want to Delta P here yes of course we can do Delta L but we can break it open because we have Delta MV we can say it's Delta and remember the equivalent of uh mass is actually I and the equivalent of V is Omega so we could say it's also Delta I Omega this is our equation right here for angular impulse now remember the angular impulse then is just a change in angular momentum that's it so what we've seen in this video can you see that we've gone over angular momentum this equation for it how it's conserved and some of the neat things it does and also just angular impulse which is very similar to the linear impulse we've learned it's just the angular version of the rot rotational equivalent