Thanks once again to Car Talk for giving me such great questions.

In the last episode, a caller asked about stopping a car. He said that when he stops, he turns the car left and right to increase the total distance over which he stops but decrease the linear stopping distance. Tom and Ray point out that this practice is a very bad idea and they don't think it would even theoretically work. So, will it?

Ok, model time. I think I already know the answer to this question, but the model might be the most convincing answer. How will I model it? With python, of course. But just to make things fun, let me use the following situation for the turning-topping car:

- Car with a mass of 1200 kg.
- Coefficient of static friction between the tires and the road of 0.8
- Initial car speed of 70 mph (31 m/s).
- I will assume the car turns in a circle of radius 15 meters until it is 10 degrees off the original line then turns back.

There is another assumption. I will assume that the magnitude of the frictional force is constant. So, as the car is turning, a component of the frictional force will be used to turn the car and the rest will be there to slow it down. Here, this diagram will help. This shows the car turning and stopping at three different times.

Here, the blue arrow represents the total frictional force. I have broken this frictional force into two components. The green arrow represents the component of friction needed to make the car turn. The red arrow represents the component of friction in the opposite direction as the velocity vector. This red-labeled component of friction slows the car down.

Maybe you can already see the problem. When you turn, you have to use part of your frictional force for turning instead of slowing down. So, although you might have more distance to stop, you will have less force stopping the car.

Ok, now for the model. Here is my numerical "recipe":

- Calculate the total frictional force (really, you only have to do this once).
- From the velocity, calculate how much of this frictional force has to point perpendicular to the velocity of the car (you know - centripetal acceleration). Note that I will adjust this amount of turning so that the radius of the turn (at that time) will be very close to the smallest radius possible. You can't just turn in a circle of whatever radius you want because the frictional force has some maximum value.
- Find out the left over component of friction that will be in opposite direction as the velocity.
- Now that I have the force as a vector - apply the momentum principle.
- Use the momentum to update the position.
- Repeat.