Conservation of angular momentum. Inorder to spin something (the flywheel if the car is in neutral) a force must be applied to accelerate it, whilst the force is applied by the pistons going up and down the conservation of ANGULAR momentum requires an equal and opposite rotation force be applied to the engine structure when accelerating. This is transfered through rubber engine mounts to the car chassis but the rubber has some give to it to let it smooth bumps so the engine twists a bit in its mounts
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