In a moving car, when brakes are applied suddenly the wheels skid.
I have these two explanations in my mind and both seems correct to me.
1. The momentum of the car must be conserved so the car continues to be in motion after the brakes are applied and the wheels skid and because of friction the car comes to rest.
2. Because of the inertia of the car, the wheels will go forward with the car skidding and it will come to rest because of friction.
But I was told that the correct explanation is the second one. I was told that it is related to the mass but I couldn't understand the explanation given to me. Why is momentum not the reason for skidding but inertia is?
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asked Jan 28, 2016 at 10:57
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$\begingroup$ Inertia tells us that the car will keep moving for some distance as long as the friction forces are finite, but momentum of the car (alone) is simply not conserved. $\endgroup$– CuriousOneCommented Jan 28, 2016 at 11:23
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1 Answer
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Momentum and inertia are closely related properties.
Newton's first law states that an object will continue in a straight line with constant momentum if no net external forces act on it.
When you apply the brakes, the road applies a net external force on the car-plus-wheels. This force will cause the car to slow down, and the road to speed up (conservation of momentum of the system car-plus-road). The transfer of momentum is given by $\Delta P = F\Delta t$ - in other words, it depends on how much force $F$ there is and for how long $\Delta t$ it acts.
The car's inertial mass $m$ multiplied by its velocity $v$ gives it momentum $P$. The fact that the force of friction$F$ is limited means it will take a finite time $\Delta t$ for the car to lose all that momentum. That is the property referred to as "inertia". The momentum of the car (alone) is not actually conserved - it is transferred to the earth (most of it, anyway - the earth moves a tiny bit because of the braking of the car)
I hope that cleared it up a bit.
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$\begingroup$ But since as there's friction, how can momentum (Earth + car) be conserved? $\endgroup$– GertCommented Jan 28, 2016 at 13:27
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$\begingroup$ @Gerr Newton 3 - equal and opposite forces for the same time. So the change of momentum of one is equal and opposite to the change of momentum of the other. But since the earth is very massive its velocity will change by the tiniest amount... $\endgroup$– FlorisCommented Jan 28, 2016 at 13:28