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14. Torque & Rotational Dynamics

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Hey, guys. So now that you've solved a bunch of rotation questions using energy and a whole bunch of other questions using torque, you might have noticed that some of these questions are very similar. For example, we did yo yo equations for both energy in torque. Now, what I want to do in this video, which is really, really critical is doing overview of these two methods. So you know which one to use in different situations. Let's check it out. So I want to remind you real quick that some linear motion problems we could solve them, using either f equals in May and motion equations. Remember, we have those 3 to 4 motion equations Kinnah Matics equations, so we could use a combination of these two methods to solve them. I'm gonna call this Method one, or we could have used the conservation of energy equation method to we. Typically, most people learned this one first, and then they learned this one. Number two is usually better because you have one equation. Um, instead of having two equations and instead of having to worry about which out of the 3 to 4 motion equations to pick from All right. So I want to show you this and linear motion, and then we're gonna bring it back to rotation real quick. Right? So if you have a block here in the block, slides on an incline on, let's assume that's frictionless. Um, there are two ways you can find the velocity at the bottom. So if you want to find the final at the bottom here, there's two ways. The first way I'm gonna use the the first way here to be f equals in May in equations. So motion equation. So the first way would be with motion and what you would do, Just like any motion problem, you would list your variables the initial the final, Um, a Delta X Delta t. Okay, lets say they start. Let's say it starts from rest. So the initial co zero the final is what we're looking for. Acceleration. We don't have Delta X and Delta T. Let's say we have the initial heights. So in the angle, let's say these were given. So from these, you would be able to find your Delta X right, because H equals delta X sign of data. So if I give you these two, you can find this one. Okay, so you would have some Delta X as well. You wouldn't have Delta Fada. That would be your ignored variable. But notice that to solve this you need to know two things. So you would know the initial you could find Delta X. You would be missing acceleration. So what you would do to find acceleration is you would right. Some of all forces equals m A. And in this case, the only force that matters here is mg X. You have MDX pulling this thing down the plane. Um, m g I will cancel with normal. And there are no other forces. So when I write some of all forces in the X axes, I have m g X equals M a x m Jax's mg sign of fada and equals m A. We're just gonna call it a the masses cancel and I'm left with an acceleration. So at this point, I know the acceleration. I can plug it in here. Okay, I know the acceleration can plugged in there, and I can use the fact that the Onley, through my ignored variables delta t to know that I have to use the second equation, which is the final squared equals V initial squared plus choue delta T It's the only equation. I'm sorry, Delta X The only equation that doesn't have delta t so I can solve here. I can cancel this out and the final velocity will be the square root of two. The acceleration is right here. G sign of data and I have Delta X. I can rewrite Delta X if we want Thio. Notice that if I rewrite Delta X, Delta X is h divided by sine of data. And if I do this, look what happens. H Sign of data. The signs cancel and I have that The final velocity is simply the square root of Chu G. Um Scored a to G h. Okay, so you could do this. Using a combination of motion equations and efficacy may kind of long. It's much better to do this using energy to do this using energy. We're just going to use the conservation of energy equation. Okay, so okay, initial Plus you initial plus work non conservative equals. Okay, Final. Plus you final Que initial is zero because it starts from rest. I have some height in the beginning. So this is MGH initial working on conservatives. The work done by you. You're not doing anything. You're just watching. Plus the work done by friction. There is no friction. So this is zero a t end. We have kinetic energy because we have linear motion. So this is half M V Final Square. And there is no potential energy at the end because you're under the lowest points, Cancel the masses and the final is the square root of two g h initial. Okay, this height here is obviously the initial I end up at the same place. So given the choice of methods, you would obviously choose the energy way of solving things because it is better. Now it's better for for velocity. If you're looking for acceleration, you would have to use at equals in May to find acceleration. Okay, So similar to how there's two ways to solve problems. We're gonna have the same thing in rotational motion. Some problems, instead of being solved in rotation instead of being solved, um, with efficacy may in motion, equations will be solved. The torque equals Alfa in motion equations, and we're also gonna have problems that we're gonna be able to solve using conservation of energy. Okay, if you have the choice, which most of the time, unfortunately, don't You're gonna wanna pick this one, right, because it's easier. But it really depends on what you're being asked or what you're being given or actually an end on what you're being given, right? So generally you will use torque equals Alfa if you're either being asked or given a or Alfa. So if I ask for a you're gonna use it or if I give you a and ask for something else, you're gonna use torque, because Alfa conservation of energy is better for problems that are asking or giving velocity V or velocity omega. Okay, you're always going to use motion equations if you're looking for time, time, Delta T or if you need time to solve the problem somehow, Okay, so you're always gonna need motion equations. So I think this is really, really important to remember, and it helps a lot make a combination of all these topics easier toe work through. Sometimes, However, sometimes, however, you're not going to have a choice. You'll be asked to do this in a specific way, even if you could have used an easier method. Sometimes the question will say, you know, using Newton's laws, which means F equals a Mayor Tory, because I often do this. So what professors will do sometimes is forced a method upon you to make sure that you can't use an easier method. Okay, so I want to do a quick example here of how questions may look almost identical but require different methods to solve. So yo yo spins around itself as it falls. Something like this Theo use falling and spinning at the same time. So it has an a n a V, and he has an Alfa and Omega find. Its acceleration after dropping 2 m, find its acceleration After dropping 2 m we cannot use. We cannot use conservation of energy to find acceleration. If you look at the conservation of energy equation, there's no a in there, right? So we would have to use to find acceleration. Ah, combination of f equals M. A torque equals I offer. Okay, The fact that it drops 2 m doesn't matter, right? The acceleration is constant throughout. This is just extra extra information. Here I oyo false. And by the way, the reason to use both of these is because the yo yo has linear acceleration in angular acceleration the same time. Okay, now here we want to know the speed after dropping 2 m. Both pieces of information are important, and we're going to use energy. Okay. And then here we want to know. How long does it take to drop 2 m? Drop 2 m is Delta y. And how long does it take? Is Delta T. Because I'm being asked for time. You have to use motion equations, Okay, But it's very likely that motion equations is not going to be enough. Because to do this, you're gonna have to have. You're gonna have to have acceleration. Let me list my five motion variables. Let me fit here. Let's say you're dropping from rest. You don't know the final velocity. You don't know the acceleration you're given Delta y and you're looking for Delta Psi. So you're gonna have to either find the final using energy or you're going to use, um you're gonna use f equals in May, and torque equals Alfa to find acceleration so that you can use motion equations so here to solve this, you're gonna use motion. Plus, and I'm either f equals in May for energy. Okay, depending which way you wanna go. All right, so let me get out of the way. So, anyway, I hope this makes sense. Um, now that we've seen these two things, you might get some questions where you sort of need to know both. And I wanted to make this a little bit simpler. You might have noticed these questions are very similar, but they do require different methods. So I think this is crucial for you to master. I hope it makes sense. And if you have any questions, please let me know. Because I wanna make sure you guys are good at this. All right, that's it for this one. Let's keep going.

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