Imagine driving in a straight line on a ice lake, when you hit the brakes, if your goal is to stay in straight path with no spinout, which wheels would you choose to have locked: front or rear? Assuming the steering wheel is kept fixed in both cases, I learned that it's better to have front wheels locked in this case. But can someone explain in accurate terms why? Thanks.
As in Gugg's answer: Let's consider the car that has slightly rotated, and let's see if the forces that the road applies on each wheel will correct it, or make it worse:
Decompose the friction of the road on the wheel in a parallel and perpendicular component. The momentum of the parallel component of the left and right wheel cancel each other out (assuming symmetrical conditions). So, for the directional stability, only the perpendicular component is important.
The blocking wheels are a regular sliding contact. Here dynamic friction applies.
The braking wheels are still turning, and so the rubber is not(*) moving relative to the road. So in the perpendicular direction static friction applies. The perpendicular component here will be greater than with the sliding wheels. It doesn't even matter if you are braking or not.
So, if the blocking wheels are at the back. A small instability will increase. Whereas, when the blocking wheels are in front, it will be instantly corrected.
(*) Now, you might say: When the car is going sideways, the braking wheels are also sliding, so dynamic friction applies on all four wheels. That's true, but the distinction between static and dynamic friction isn't as black and white as the theory suggests. For a very small rotation, the sliding is minimal and friction is still higher, and that is enough to immediately correct it.
A wheel has traction in two component directions: both parallel and perpendicular to the direction of the movement of the car. The perpendicular components, by definition, won't do anything different for the direction of the car. But the parallel components will cause locked wheels to decelerate less in the parallel direction than unlocked (but significantly braking) wheels. Therefore, the rear wheels locking will (as soon as the car is/becomes a little bit angled) cause more rotation than the front wheels locking. That's why.
I think because if you lock rear wheel's and start sliding the car on the ice the front wheel will suffer a frictional force whose line of action could deviate from a straight line parallel to the central line of the car to any other direction causing a resultant force in either direction's which could spin the car. On the other hand if you lock the front wheel the car will start sliding and the rear wheel will suffer a frictional force but in this case the force will align the car in a straight line as it will be a pull force and will keep the carr straight and prevent it from a spinot.
For the same reason Michelin recommends always putting new tires on the back first Tires 101 you any slipping (non-rolling) to occur on the front if stability is required.
So to brake on ice and not loose control (spin out) make sure the front tires lock up first and the rear keep rolling maintaining traction. It is the same reason people put caster wheels on the front of a grocery cart and not the back.