 In this video, I want to talk about disc and drum brakes. So when we talk about a disc brake, it's effectively the same thing as a disc clutch. We're still taking two surfaces and pressing them together to try to bring them to the same speed. It just happens that one of those two surfaces is has a speed of zero. So we're still trying to accomplish the same thing. And really our analysis of that doesn't doesn't change anything. One thing that's slightly different from how we looked at it when we talked about disc clutches is that generally we use like a caliper, which has a brake pad. That's obviously not a full circle. Really just for the purpose that we can prevent heat buildup in the material by giving a smaller surface area so that it's easier for that heat to dissipate more air flow and things like that. So I want to talk about a slightly different version, but the same principle and that is conical disc brakes or clutches, same general principle. So in a conical system, we have the same idea in that there's a rotation and these two things are being pressed together. But now the surface where they make contact is at an angle rather than two flat surfaces being pushed together. They're at an angle. So when they come together, it's like that. And that changes slightly then how we go ahead and analyze these two things. So if I take kind of a view, another view of this, and I'm going to draw in a centerline here. Now I have an angle of this surface, which I'm going to note as alpha. And I have similar to when we talked about disc clutches, I have a contact, a differential contact area here that I can use for my analysis, where there is an RI on this inner side. If I extend this line over, I'm measuring RO. And the width of my little differential unit here, my differential area is slightly different, but not much. It's dr over sine alpha. So not terribly different, just a modification to project that area onto that surface. So that means when I write my differential area, I'm getting two pi r dr by sine alpha. Now I can look at the force of that interaction between the two, but now I'm going to write it as a normal force, just to indicate that it's normal to the surface. And when I do that, I can say two pi, I'm going to substitute in RI here like we did before. dr over sine alpha. And I'm going to multiply that by Pmax. So I'm again taking that idea that the maximum pressure occurs at the inner radius due to there being assumed a uniform wear rate. Then I can take and find torque by saying it's equal to dn mu r. So I get two pi Pmax mu ri dr by sine alpha. So I have a lot going on in there. Now I can carry out my, oops, I missed an r in here. Let's just sneak that in there. So now I can carry out my integration much as I've already done before. And I can get pi ri Pmax mu ro squared minus ri squared divided by sine alpha. And performing again a substitution for Pmax, I get f mu by two r naught minus ri over sine alpha. And obviously what we're ending up finding here is that nothing has really changed from when we had a clutch with two discs pressed together like this. All we've added in is this value of sine alpha. And the reason that this is actually beneficial, if we kind of think about it a second, is if I look at this sine alpha, my angles are relatively speaking going to be small for that alpha angle that I have on my drawing here. And the sine of that value is going to be some number less than one, right? So if that number is less than one, that means it's going to be increasing my torque. So my torque that I can transmit between these two things being pressed together is greater than what it would be for just two flat discs being pressed together because of the cone. We have kind of a wedging action going on here is as one of the surfaces gets wedged into the other one, you get a higher torque for the same amount of force being pressed together. So that's one reason why we might actually want to use these sorts of things. All right. So that's the important equation when we're talking here about conical brakes. Of course it applies if we were somehow using a conical shaped clutch or anything like that. It's all the same, same general analysis. Now I want to talk briefly about drum brakes. I'm not going to go into detail on them. Let's draw that, write that a little better. So drum brakes can kind of, can come in a couple of different formats. We can have an external shoe. So an external shoe we have rotation of a drum and then we have the shoe located around the side. Often there would be two of them, not necessarily, but just as an example. And then we have a support structure which provides the structure that holds the shoe. A linkage here which connects to, oops I drew this a little bit wrong, but we have a handle here presumably or something, some sort of force input and a linkage here. And then the idea would be if I apply a force down it's going to pivot on this connection, pull this linkage and snug these two shoes in on the drum in order to provide the stopping friction. Of course I could also have an external shoe form where I just have a single shoe maybe on top pushing down to provide that stopping friction. I can have what we would call like a short shoe which is a small pad or a long shoe which wraps further around the drum. A variety of different formats for that. It's labeled this just for clarity. So if we were looking at this you know you can kind of imagine how we might analyze it whether we have the force of friction interacting between the shoe and the drum and then we have a big linkage system which we can analyze using free body diagrams if we broke this all into its component pieces and analyzed it by free body diagrams we'd get our our forces that way. We can also have an internal shoe so suppose we have a drum that's just rotating, that's not good at all, try again. So we have a drum which is rotating itself and our shoes are mounted inside adds in here so they're going to make contact with the inner surface of this rotating drum and then we can put a hydraulic cylinder or something like that between these two rigid frames so when that hydraulic cylinder is activated it pushes the two shoes out to make contact with that inner rotating drum and provides the the stopping force that way. So kind of a similar idea to the external shoe but of course just mounting the shoe on the inside and kind of accomplishing the same thing. Applying the force outward pressing those break shoes against the inner inside of the drum and therefore leading to a stopping force that way. All right so I'm going to go ahead and stop there.