The car comes to a sharp turn in the road
- Due to inertia, the car will continue to proceed in the direction it was going in before the turn. Unless the car can generate enough friction with the ground to pull it in the correct direction, its momentum will continue to carry it forwards.
The car has to stop quickly
- Again, inertia due to the car's mass will cause no sudden change in momentum due to a lack of friction between the car and the icy road. The car will simply keep its velocity without any change unless proper backward force breaks its tendency to keep its current momentum. If the car was lighter and/or had tires that could pull on the icy road, then it could probably stop without much of a problem, as it won't have as much inertia (it has less mass) and it would be able to generate enough of a forward force (friction) to pull itself forward.
The car is stopped and has to start moving
- Without enough friction between the car and the ground, there will be no change in momentum. It will keep its current velocity, 0, without enough of a forward push to break the force provided by its coefficient of friction with the ground.
Note: The coefficient of friction is not an actual force acting on the car unless there is an outside force attempting to break the car out of equilibrium. It is then that the friction acting on the car while at rest will come into play.
