 So what forces are acting on the car? Well, there's gravity pointing downwards, of course, and there will be a normal force applied by the track on the car. This normal force points perpendicularly to the surface, like any normal force. Since there's no friction, that's it. Those are all the forces acting on the car. As the car is following a circular path, there must be a force pointing radially inwards. Looking at our three-body diagram of the car, the centripetal force responsible for uniform circular motion must come from the horizontal component of the normal force. So that's what we need to find. Let's start with what we know. We know that the force due to gravity is mg and it points directly downwards. We also know that the car isn't lifting off into the air or sinking into the road beneath it. That is, the vertical forces must balance. To get the vertical components of the normal force, we can draw out a vector triangle, showing both the vertical components and the horizontal components, which together add up to the total normal force. The angle between the normal force and the vertical is theta, the same as the angle of the banked track. This can be shown using geometry. This means that the vertical component of the vertical force is equal to the normal force multiplied by car's theta, and the horizontal component that points radially inwards is equal to the normal force times sine theta. To get the horizontal component of force, we need to calculate the normal force, and we can do this by balancing the vertical forces acting on the car. As there is no net vertical acceleration, we know that the gravitational force is equal to the normal force times car's theta, and therefore the normal force is equal to mg divided by car's theta. Now let's look at the horizontal components. We know, as the car is undergoing uniform circular motion, that the centripetal force is equal to the horizontal component of the normal force. Calculating, we find that the centripetal force is equal to mg sine theta divided by car's theta, which is equal to mg times tan of theta. If we want to find the velocity of the car, we can plug in our uniform circular motion equation, and find that the velocity is equal to the square root of rg tan theta. Let's plug in some values. We'll use a car mass of 1200 kilograms, a banking radius of 20 meters, and a bank angle of 5 degrees to find the centripetal force and the car's velocity. The centripetal force is equal to 1029 newtons, and the velocity is equal to 4.1 meters per second, or, in a more typical unit for cars, this is equal to 14.9 kilometers per hour. Now in reality, you'd have a combination of the normal force and the friction force providing the centripetal acceleration. However, the calculations we've seen in this video give you a worst case scenario, where there's no friction and you have to rely entirely on the banking of the track.