/sci/ - Science & Math

The answer has almost nothing to do with gyroscopes, and even without gyroscopes it's fairly simple high school stuff - if you paid any attention during the most elementary physics courses in motion available you would know the answer.

As the bicycle tilts to any one side, it wants to steer in that direction, because the wheels are circular. Anything going in circular motion has some centripetal force that keeps it in that circular motion - in this case, friction on the back and front tires. Friction points towards the center of the circle, and because the center of the mass of the bicycle is above the bike, the resultant torque acts to straighten out the thing.

You can mess around with varying the parameters and you'll notice that tighter circles mean greater force, so that leaning more will actually force you to straighten more, and leaning less will cause you to straighten less - the torque is a restoring force. Similarly, increasing velocity increases force by a factor of velocity squared, so going just a bit faster increases the correctional force by a factor of 2, which explains why it's so difficult to stay upright at a crawling speed and much easier once you get up to speed.

As long as the correctional torque is greater than the torque of gravity, then the bike will stay upright. You should note that this does not mean drive a heavier bike - torque provided by gravity also depends linearly on m, and will act just as well against you as for you in terms of stability.