When the piston is going up it is compressing the air in the cylinder which slows down the engine. Then when the piston gets to the top it ignites the fuel and the piston is pushed back down. This constant slowing down and speeding up is felt as vibration. At higher speeds you do not notice it as it comes much faster and the engine have components balancing the vibrations to reduce them. But at slow speeds the engine can almost stop as it is compressing and then speeding up when the fuel detonates so you get a huge difference in speed through the stroke.
The engine stops when it no longer have enough speed to compress the air in the cylinder. When the air provides too much resistance it can stop the engine before it gets to the top. When the car is in gear and you are driving along the engine can get much slower without stalling because the entire car is pushing the piston up. It is not just the flywheel that have to stop but the entire car. But on the other hand the engine is not as powerful at lower speeds and the car provides a lot of friction for the engine to overcome. So when the engine speeds gets too slow the engine will just go slower and slower as the car slows down even with full throttle.
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