 One of the most common examples of uniform circular motion that you may even have encountered this morning is a vehicle such as a car, bus, bicycle, quad bike, or tractor turning around a bend. In this video we'll look at motion around bends and why the turns on race tracks are banked at such steep angles. Firstly let's make sure that we're actually dealing with uniform circular motion. It's straightforward to see that a car traveling around a roundabout is following a circular path. But what about a car going around a bend or making a turn? This path is clearly not a circle, but it turns out a section of the turn is approximately circular. So if the car is going at a constant speed then we can analyse this part of the turn. We know that when a car turns something must be causing the centripetal force. That something is the friction between the tyres and the road. The same force that keeps you from pushing a car sideways allows cars to turn around bends. Now at some point friction won't be strong enough to oppose the applied force and the car will start sliding. This occurs at the maximum friction force. The maximum friction force dictates the faster speed a car can travel around a bend. In this example we'll call the friction force F subscript F. We know that the car experiences a centripetal force, so F subscript C is equal to the mass times the velocity squared divided by the radius. And this centripetal force is provided by friction. So the centripetal force is equal to the friction force. Therefore the speed is equal to the square root of the friction force times the radius divided by the mass of the vehicle. But we also know that we can write friction in terms of the normal force and the coefficient of friction. So we know that the friction force is equal to the coefficient of friction or mu times the normal force. Since the car is not accelerating vertically up into the air or down into the ground the net vertical force is zero, so vertical forces must balance. This means that the normal force is equal to the weight, on flat ground at least. Rearranging these equations we find that the speed can be written as the square root of mu times gr