Basic Physics Law: Why Brakes Make Car Front Go Down, Rear Go Up

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Eagle Eyes
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When we hit brakes on a forward moving car, the front of the car moves down and the
rear moves up. Why?
 
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The reason there is torque is because the point of braking is not aligned with the centre of mass of the vehicle. The braking is applied at the bottom of the vehicle. No such braking is applied at the top of the vehicle. So it wants to rotate.

Let's say the brakes, rather than being applied to the road, were applied to surfaces than ran through the centre of mass of the vehicle. Pretend there are guardrails running along the sides of the road at about 3 feet high. The brakes grab those instead of the road. Because the centre of mass of the vehicle is about 3 feet high and the application of braking is also about 3 ft high, there's no torque. The car's nose does not dip.
 
The main creation of torque is due to the ground applying a backwards force at the contact patch of the car (the bottom of the car as mentioned above), and the corresponding forwards inertial force due to braking at the center of gravity of the car. The distance from ground to center of gravity times the braking force is the torque due to these forces.

There's also a pitch down torque due to the brakes themselves. The front brake caliper would try to raise the rear end, the rear brake caliper would try to lower the front end, there'd still be a re-distribution of downforce on the tires under braking.