Comment by vvilliamperez

I ride and work on motorcycles a lot.

tl;dr: Front wheel fork angle causes uprightness, the overall cause of turning is due to tire shape and contact patch at lean. Countersteering is the input to start and maintain leaning.

Bicycle and motorcycle physics have a lot of different forces at play, but the main one for keeping the bike upright is the front wheel, causing corrective steering at lean.

When a bike starts to fall, the rake angle causes the wheel to "self correct" and steer the bike towards uprightness. With speed, the bike wants to stay upright and will self correct.

To steer at low speeds (most bicycle speeds), you actually turn the wheel in the direction you want to go very briefly, "fall" into a lean and switch quickly to counter steer in the other direction, keeping the bike upright.

At high speed it's a bit different. You don't need to initiate the turn. You can just skip straight to counter steering, which forces a lean and causes a turn. At speed you are constantly upright, so you need some input to tilt the bike.

The effect of leaning to the right with the wheel self-correcting left, is an overall arc to the right (vise versa).

As for gyroscopic forces, these are at play but the force is negligible for keeping the bike upright. Heavier wheels have higher angular momentum, making the bike a bit harder to force a counter steer. They also affect how quickly a bike can accelerate given a certain force.

Cool video: https://www.youtube.com/watch?v=vSZiKrtJ7Y0&t=3s