Final answer:
The car rocks in the opposite direction of the engine's rotation when started in neutral due to conservation of angular momentum, but this is quickly dissipated by frictional forces, so the angular momentum is not conserved for long.
Step-by-step explanation:
When you start the engine of your car with the transmission in neutral, the car exhibits a rocking motion opposite to the engine's rotation due to the conservation of angular momentum. The principle states that if no external torques act on a system, the total angular momentum of the system remains constant. Since the engine's rotation is one part of the system, another part must rotate in the opposite direction to balance out the total angular momentum. This reaction is the car's body rocking in the opposite direction.
However, this conservation of angular momentum is not maintained for more than a few seconds. Frictional forces, especially from the car's suspension system and tires, quickly dissipate this motion, bringing the system to a rest. Thus, while the angular momentum prompts an immediate reaction, it is not conserved in the car for an extended period due to these external torques.