Hey, guys. So in this video, we're going to start talking about torque acceleration problems, also known as rotational dynamics problems, where we have 2 types of motions. What that means is that on top of having a rotation, we're also going to have objects moving in a linear direction. So it's going to have a combination of both of them. Let's check it out. So remember, that when we have problems where a torque causes an angular acceleration, where torque causes an angular acceleration α, we use the rotational version of Newton's second law. So instead of F=ma, we're going to write torque, sum of all torques equals Iα. Okay? So then when we have torque α questions. That's how we solve it. But in some problems, we're going to have more than just α. We're going to have rotational and linear motion. So for example, here in this picture, if you have a block that's connected to a pulley, if you release the block, it's going to accelerate this way. But because it's connected to the pulley, it's also going to cause the pulley to accelerate this way. So the block falls in linear motion and the pulley accelerates around its central axis in rotational motion. We have both. And in these questions, we're not going to use just torque equals Iα, but instead, we're going to use both torque equals Iα and F=ma. Okay? So we're going to write sum of all forces equals ma for each acceleration we have, and we're going to write sum of all torques equals Iα for each α that we have. So for each a, we write F=ma and for each α we write torque equals Iα. Now what do I mean by each a and each α? You have to count how many motions exist in the problem. Here I have one object with one acceleration, one type of motion, linear motion. And then here I have another object with another type of motion. So there's 2 motions in total. Okay? But if you had more types of motions and I'll get to that in the example below, you would use more than just 2 equations. Alright? We'll get to that. When you do this, when you combine F=ma with torque equals α, you end up with an a and an α. That's two variables. One of the techniques we're going to use to solve these questions is instead of having a and α, we're going to replace α with a. And by doing this, instead of having a and α, I'm going to have a and a. Imagine in this, second equation here. Imagine if that α somehow became an a, then you would have a there and a here. And that's good because instead of having 2 variables, you now have one variable. This is a key part in solving this question is going from, α to a. Okay. And the way we do this is by remembering that a and α are connected. They're connected by this equation. a=rα, where r is the distance between, it's the distance between the force and the axis of rotation. So it's our r vector from the torque equation if you remember. So where r is distance, I'm going to call this distance to the axis. Okay. Distance to the axis from the force. Okay. But this is actually not the equation we're going to use because what we're looking for is we're trying to replace α. So what we're going to do is we're going to say α=a/r. Wherever we see an α, we're going to replace it with a/r and that's going to simplify. Okay. So we're actually going to use in these questions a combination of 3 equations. F=ma, torque equals Iα, and we're going to use this one here to link the 2, the 2 first equations. Alright. The last point I want to make here is that the signs for a and α, as well as the signs for v and ω must be consistent must be consistent. What do I mean by that? So I'm going to give you, one example that allows me to talk about these 4 variables. And it's this one. You have a disc that's rolling. Actually, let me draw it. You have a disc that rolls up a hill. Okay. So imagine that if you are going this way. Right? And then you're going this way. Okay. Your I'll draw it over here. You're spinning like this and then you go up the hill spinning like this. So that's your v and this is your ω. Okay? But if you're going up a hill, gravity is pulling you down. So your acceleration is downhill. It's going to be like this. And a and this means your α is actually like this. Okay. Because if your velocity if you're going up like this, means that your ω is like this. Then an acceleration that's down, means that your α is like this. Alright. And all of these signs have to be consistent. So in most of these p