Title says it all although by “moving” I do not mean the usual zipping around where the gyroscopic forces of the wheel spinning serve to keep you upright.
Rather I mean I can balance on my bike with little trouble (perhaps a tad wobbly) if the bike is just barely inching forward. Once I come to a complete stop though I can’t maintain balance for very long before tipping.
I cannot imagine the gyro forces are anywhere near significant in this case so it is (probably) something else.
When you’re moving, you balance by turning into your fall. When you are stopped, you cannot do that.
minutephysics did a good video on bike stability.
This. Somewhere out there is a demonstration video of a “bicycle” where the wheels have been replaced by ice-skate blades. There’s no propulsion, other than a good initial launch, but it showed that ordinary self-stabilizing steering geometry (and/or a pilot who is familiar with riding a conventional bicycle) is adequate to maintain stable forward movement, no gyro-stabilization required.
You can, but it takes practice and a trick. Imagine you’re stopped, feet on the pedals, butt up out of the saddle, with the handlebars turned maybe 60 degrees to the left.
Now suppose you start falling to the left. How do you arrest your leftward fall? Easy, just pedal forward a smidge; the front tire’s contact patch will move to the left, arresting your leftward fall.
Now suppose you start falling to the right. How do you arrest your rightward fall? This is the trick:
keep those handlebars pointed 60 degrees to the left.
Lock the front brake.
Gently push the handlebars away from you. With the front brake locked, your body starts moving backwards (don’t let go of the handlebars).
While your body is still moving backwards, release the front brake, and now pull the handlebars toward you. The bike will begin moving backwards with your body, but because you’ve got the handlebars turned to the left, the front contact patch will move to the right, arresting your rightward fall.
(If you’re riding a fixie, you can skip steps 2-4 and just pedal backwards.)
There are plenty of YouTube videos of guys doing trackstands in which they inevitably creep forward very slowly because the rely on pedaling forward and steering for correcting falls in both directions - but if you master the above technique, you can idle indefinitely on the same small patch of pavement, zero creeping forward required.