Spinning mass has rotational inertia. In this case the bicycle tires are rotating quickly so they have lots of inertia. The more inertia something has the harder it is to change that inertia. With the rotating mass it’s happy to move along the plane that it’s rotating in (ie forward of backward) because that’s a small change to inertia. Twisting the plane of rotation requires lots of force because it’s a big change to inertia. Falling over requires you to twist the plane of rotation from vertical to horizontal.
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