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Current time:0:00Total duration:7:17

Video transcript

let's talk a little bit about the conservation of angular momentum and this is going to be really useful because it explains diverse phenomena in the universe from Y and ice skaters angular speed goes up when they tuck their arms or their legs in all the way to when you have something orbiting around a star and the closer and closer it spirals in it seems like it's rotational velocities angular speed is picking up and it starts to rotate faster and faster around the body you'll see that if you see simulations of estra astronomical phenomena so the big picture here is is if we have our initial angular momentum for a system and we'll think about that a little bit no matter as long as the system has no external torque applied to it then your final angular momentum is going to be the exact same thing and so one way to think about it let's imagine that I have some type of spinning thing over here I have some type of mass let's say it's on a table I'm looking from above and a point on the outside of this disc is spinning in this direction with a velocity of magnitude V and let's say that there's a clump of clay of orange maybe it's play-doh or clay or something and it has a velocity going in this direction it's not a collision course with this object and let's say it has a velocity of 5 V and so if we think about the this disc clay clump system and so you always have to specify what system you are talking about so if you think about this entire system how does the angular momentum change before these two things collide and then after these two things collide so actually let me draw that after the collision scenario so the after the collision scenario it looks something like this where the clay has now clumped on to this and now they are going to be rotating together and I haven't even told you the mass of this disc or the mass of this clay so it would be unclear in which direction they would now be rotating but how is the angular momentum going to change from this state from the initial state to the final state pause this video and try to think about it well you might have guessed since we said look we have this whole system and we're not applying any external torque to the system our angular momentum is going to stay exactly the same now we have to be careful if I told you the system was just this disc not the clay clump that's on a collision course with it then the angular momentum for the disc would change but why is that does that defy the conservation of angular momentum no because this clay clump when it collides would be providing an external torque to the system if we define the system to just be the disc but since it's the disc plus the clay clump and we have no external torque to that combined system then our angular momentum is not going to change now that we can appreciate that angular momentum is constant as long as that there is no net torque applied to the system let's think about the famous situation where an ice skater angular speed goes up as they tuck in their arms and you can do a less graceful version of this on an office chair where if you sit on the office chair and you begin spinning this is my office chair and if you stick your legs out at first you're going to spin slowly but then if you tuck your legs in then you're going to start spinning faster you're going to have a higher angular speed now why is that well to appreciate that we can think about the formula for angular momentum so the formula for angular momentum L there's a couple of ways we can or several ways that we could write that we could write that as our moment of inertia I times our angular speed times Omega and this might look a little bit foreign at first to you but it has a complete a now analog when we're dealing in the linear world here we're rotating in the linear world we say that linear momentum is equal to mass is equal to mass times velocity and the reason why we have an analogue here is mass can tell you about inertia of an object how much force you need to apply to accelerate that object F equals MA well moment of inertia you have something similar going on but instead of thinking about how to just linearly accelerate something this tells you how hard is it to get angular acceleration how much torque do you need to apply instead of just how much linear force you to apply and instead of velocity you have angular speed and sometimes this is called angular velocity as well but this by itself you might say well this doesn't help me when I'm tucking in my knees when I'm on an office chair or the ice skater tucking in her arms well to think about that we just have to appreciate that the moment of inertia can be expressed as M times radius squared M R squared and then we still have our Omega right over here so this is another way of writing angular momentum and so when a skater tucks in her arms her mass is not changing that is staying constant but remember the radius one way to think about it a little complicated when you're thinking about a human body system in a simple sense if you just have a point mass rotating around a point like that then this is the radius but if we're dealing with a more complicated structure like a human body you can imagine the radius as being indicative of the average distance of the mass from the center of rotation and so when the figure skater tucks in her arms that average distance goes down and so when she tucks in her arm this goes down but if this part goes down but our angular momentum stays constant because we have no torque being applied to the system no net torque being applied to the system well then this needs to go up in order to keep that angular momentum constant and that's exactly what's happening the angular speed picks up just as the radius goes down now this also explains why if you have let's say that's some type of a planet and you have a rock or something orbiting it as this gets closer and closer to the planet it's going to its angular speed is going to go higher and higher and higher why is that well because when you have a high radius so here your radius is higher and so your angular speed might be a little bit lower but then when you're closer in when you're closer in your radius has gone down and so your angular speed has to go up to make for up has to go up to make up for it I'll leave you there I encourage you to have fun spinning on office chairs