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Why does a car nose up when accelerating and nose down when braking?
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There are different ways to answer this question. An elegant one consists in using Newton's third law. Do you know what torque is? If so, think of the torque applied to the wheels when accelerating and when braking.
I believe it is because there is a Force. When you accelerate or decelerate there is a Force that you can feel. F=ma
Because the force accelerating the car is not applied at its center of mass, but displaced beneath it, where the tires meet the road. This results in not only a forward acceleration of the COM, but a torque about the COM that tends to rotate the car.
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