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Centre of mass of a system cannot change its state of motion, unless there is an external force acting on it. Yet the internal force of brakes can bring a car to rest. Then what stops the car?

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Using your terminology, the brakes aren't a "internal force". You can think of the wheels as attached to the road rather than attached to the car. The brake pads are attached to the car and rub against the wheels attached to the road. – Brandon Enright Dec 22 '13 at 5:55

It appears that you are only considering the system consisting of the vehicle, i.e. car+wheels+brakes, as @user31782 has pointed out. Examining only this system, there is no way for the car to stop: it is traveling through space at a certain speed, and that speed is independent of the spinning wheels; if you apply the brakes the wheels stop spinning (and transfer their angular momentum to the car, sending it into a forward tumble) but the car continues sailing through space. Let's say for the sake of a convention that the car is flying "left" though space, just so we have a direction to talk about.

Along with the car, there is another body to consider: a planet under the car, which is also flying "left" through space at the same speed as the car. This planet is also spinning and is held close to the car by the car's gravity, so that the surface of the planet is pressed against the bottom of the wheels. However, the planet is spinning at just the right speed so that the surface of the planet is traveling "right" through space at the same tangential speed as the bottoms of the wheels are traveling "right" through space. (Remember that since the axle of the wheels is attached to the body of the car, the axle and car travel at the same speed; and because the wheels are spinning, the top of the wheel is traveling forward faster than the car and the bottom of the wheel travels forward slower than the car, i.e. is traveling "backward" with respect to the car.) Because the planetary surface and the wheel bottom are traveling in the same direction at the same speed, there is no friction between them and thus no forces. The car continues to travel at the same speed in the same direction.

Now you press the brake pedal and stop the wheels from spinning. Because the wheels and brakes are part of the same system as the car, stopping the wheels doesn't change the speed of the car (though it would transfer the angular momentum from the wheels into the car, but we'll ignore that here). This realization is why you ask what stops the car: the brakes are part of the system, so they can't effect the speed of the system.

BUT: The surface of the planet (which is not part of the system) is still spinning; furthermore, because it is spinning against the stopped wheels, and pressed to them by gravity, there is now friction between the surface of the planet and the car. The car is traveling "left" through space, but the surface of the planet is traveling "right" through space with respect to the car; so the friction between the wheels and the planet will also push the car to the "right," slowing and eventually stopping it in place on the surface of the planet.

In other (fewer) words, while the friction between the wheels and brakes is an internal force that does not affect the speed of the car, the friction between the ground and the wheels is an external force and does affect the speed of the car.

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Friction. The wheels are one system, the brakes are another. Relative motion between the wheels and the brakes is what causes friction, and this reduces the angular speed of the wheels. A reduction in the angular speed of the wheels requires the car to slow down too, assuming the wheels don't slip.

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if we consider our system to be (Car+wheels+breaks) then without skidding of tires how the system comes to rest with only internal friction forces? – user Dec 22 '13 at 12:50
Who said the entire thing is one system? I'm saying the wheels are one system, the brakes are the second system – Pranav Hosangadi Dec 22 '13 at 18:38
could you explain my point in your answer ,for i have the same question in my mind as of OP depicted. – user Dec 23 '13 at 12:57
@anupam, see Brandon's comment to the original question above. – Pranav Hosangadi Dec 24 '13 at 18:33
Should i ask the same question as that of OP by mentioning that the system is (Car+wheels+breaks)? – user Dec 24 '13 at 18:39

I would treat the car and the Earth together as a system. No internal forces can change the momentum of that system. However, the brakes can change the relative motion of two parts of that system - stopping the motion of the car with respect to the Earth.

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