[ska]

  Why does it cause the front wheel to rotate away (right) ?

Answer is : "it's complicated" , which is why this subject causes confusion. There are many arguments about the exact dynamics (combinations of gyroscopic effects, torques, center-of-mass motion), but empirically it is pretty clear that two wheeled vehicles like bikes/motorcycles do not turn without counter-steer.

[jonsen]

Not at all complicated. A bike is made so that the front wheel will turn in the same direction as the bike is leaned. This has a simple stabilising effect. Bike leans right, front wheel turns right, increased centrifugal force from the sharper turn will unlean the bike to the left.

[buvanshak]

> Bike leans right, front wheel turns right

Agree. But this is not what the other person is saying.

[ska]

Except, it doesn’t at first. Which is why this is counter intuitive.