ï»¿ >> So, let's draw a top view of the car. So, we've got a car moving in a circle. Here's our car. Going around. This is the top view. And if it's moving around at constant speed-- Then there is a force that is keeping it in that circle. We know that that force has to be pointed directly towards the center of the circle, even though the car is moving in this direction. What is that force? OK. It is centripetal force, but centripetal force is just a description for whatever real force is keeping it in the circle. What's the real force keeping it in the circle? Static friction. Right? The tires on the road have static friction and that's what is keeping it in a circle. So, let's think about the work now. Work is the integral of F dotted with whatever pass-- whatever path you have. OK? But we know what path it's taking at that instant of time, it's just the velocity times that little chunk of time. And, therefore, this first part becomes F sub s. We have the cosine of the angle between them, which we said was 90. We have the velocity v and we have a dt, but the cosine of 90 is 0. And so static friction does no work. We said this last time, but we're saying it again. Even though the object is moving, the static friction between the wheels, between the rubber and the road, that does no work. And here's kind of the cool general idea. If you have an object that's moving in a circle, like a ball on a string and there's tension in that string-- And this thing is moving around at constant speed, then the tension T does no work. OK? If this is the top view of the ball going around, the tension T doesn't do any work either, which means the ball doesn't speed up or slow down. But it's even more general than that. Let's say I take an electron and I apply a magnetic force to that electron. And that thing is moving in a circle. The magnetic field also does no work. And you're going to learn about this in 196. If you have a charged particle in a magnetic field, that force is always at a right angle to the motion, which means the magnetic field doesn't do any work. OK? And so now when you get to 196 you should immediately ask the question well, wait a minute, I know if I take a magnet and I pick something up, that object can actually levitate up off the ground and grab onto the magnet. Surely that magnetic field did work. It didn't. OK? It didn't do any work. Magnetic fields do no work. OK. So, let me ask you a question about your car then. If we just said that static friction does no work, let's think about what happens when you stop your car. So, let's say we're on a level road and we have a car and we're driving along and then we want to come to a stop. There is clearly a change in kinetic energy here, right? We had a lot of kinetic energy and then we have no kinetic energy. So, what did the work? If static friction did no work, then the wheels as they roll on the cement, that can't be doing the work to stop the car. So, what did the work? What do you guys think? What did you say? The brakes. Tell me about brakes. [ Inaudible Speaker ] What's your name again? >> Alex. >> Alex, hit your mic button Alex. Let's have a chat. So, Alex, you said that the brakes must have done the work. Everybody knows that you stop your car you push on the brakes. What is inside the brakes? What happens in the brakes? >> The-- there's a clamp that applies-- the 2 brake pads push the brake, it applies pressure onto the wheel, the center of the wheel, and it slows the wheel down to where-- to the point where your car starts slowing down and stops. >> OK. That's exactly right. So, the brakes in your car look like this. There is this big metal cylinder called a rotor and this rotor is attached to your wheel and it's spinning around. And then you have these pistons that push onto the rotor and that's where your brake pads are on the ends of those pistons. So, as this rotor spins around, the brake pads come in and grab onto the rotor and that is kinetic friction. OK? So, the brakes actually work due to kinetic friction. Just like when we had that box sliding along on the surface, it was kinetic friction that slowed it down. The brakes in your car work on kinetic friction. That metal rotor sliding past the pads causes kinetic friction. What happens in your brakes then? When you stop your car, that energy had to go somewhere, right? We had kinetic energy, it went away, it must have gone somewhere. Where did it go? Into heat. Brakes get really hot. And you can test this out yourself, but be careful. OK? If you stop your car at the end of the day, get out of your car, walk to the front, look inside your front wheel and you'll see this big silver metal disc, the rotor. Lick your finger and then touch the breaks and it'll go psst [phonetic] and it'll make the steam burn off your finger. OK? And you won't burn your finger if you just do it very quickly, but those things get really, really hot. They get so hot that the whole thing melts and this is what happens when your brakes fail and you run out of control. All right. Good for today. I'll see you guys on Friday. If anything's not clear, come visit me in office hours. Cheers.