When it’s leaning, it’s turning. When it’s turning, momentum wants the motorcycle to keep going in the direction it was going (straight: objects in motion tend to stay that way), but the wheels are making it turn.
From the perspective of someone sitting on/in the vehicle, you feel that “wants to go straight” against the turn as a force towards the outside of the turn.
The way to counteract that force on a motorcycle without tipping over is to be leaning into it. The faster you go and sharper you turn, the more lean you need. Without it, you tip over.
It’s kinda like how in a stiff wind you need to lean into it to not fall over. In a tight turn you need to lean into it to not fall over.
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