How is conservation of momentum present in an airbag?
In the same way it is present everywhere. If you want a more specific answer you must specify more accurately why you think there would be a problem.
I think I know what you are getting at.
When your body is brought to a halt in an accident, you need to get rid of all that momentum. The Impulse (change of momentum) needed is Force times the Time the force acts. An airbag extends the time considerably, compared with hitting the windscreen or even hitting the seatbelt. The force on your body is reduced proportionally so you may step out of the car, unhurt when the other passenger could have to be scraped off the windscreen. You both 'had' the same amount of initial momentum and end up with none.
In addition to extending the impulse in time, the airbag extends it in space, thus reducing the pressure at any specific point (e.g. nose on steering wheel) by increasing it at all the other points.
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