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If I ride a bicycle on a moving sidewalk so that I am not in effect moving at all relative to the ground, will I fall over?

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    $\begingroup$ That depends on whether you can ride a bicycle! If you can do it on a normal road, you can do it on a moving sidewalk. See this video from the Technical University of Delft's bicycle lab - they even pulled the string to make the bike wobble - no problem.\ $\endgroup$ – Floris May 22 '16 at 2:20
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    $\begingroup$ youtube.com/watch?v=-jh-5TYAtJI First 10 seconds of this show a cyclist riding on an inclined treadmill at the University of Bath in the UK. He's not falling over, so its possible to ride like this. You still may fall over if you're not able to ride a conventional bike. $\endgroup$ – Criggie May 22 '16 at 3:13
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    $\begingroup$ Ask a crew member on a huge tanker; they've used bikes to move from one end to the other... $\endgroup$ – DJohnM May 22 '16 at 5:44
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What keeps a bicycle up is a variety of things, but it all comes down to the front wheel, which can move left/right. The bike is always out of balance, and if it starts to fall to the left you unconsciously turn to the left, which moves the point of support (the wheel on the surface) to the left, which arrests the fall and may start the bike falling to the right. Then the reverse happens.

You can see this when riding a bike or motorcycle. The front wheel makes small steering motions all the time. An easy way to see this is to try to ride along a straight line marked on the pavement. You cannot do it for very far without turning off to the side.

So it does not depend on your relative motion to the ground outside. It depends on your relative motion to the surface that supports you, so that you can make these small steering changes to move your point of support left/right. In fact, there are gadgets you can buy that simply put your bike on rollers and you can ride indoors, as in this video.

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    $\begingroup$ "You cannot [ride down a marked line on the road] for very far without turning off to the side." Actually, it doesn't require a huge amount of skill to ride down a marked line for as far as you like. $\endgroup$ – David Richerby May 21 '16 at 19:26
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    $\begingroup$ Yes the turning of the front wheel is crucial, but it's not just about the rider unconsciously turning it. Many bikes will stay up by themselves if moving at a moderate speed. The movement of the bike automatically turns the handlebars to steer into the direction of lean. $\endgroup$ – bdsl May 21 '16 at 20:38
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    $\begingroup$ Actually, it has been shown that gyroscopic precession is not necessary. The real force in play for a bicycle is due to the angle of the fork; when the bike is at an angle, there is a force on the wheel that will "steer into the turn" and restore stability. $\endgroup$ – Floris May 22 '16 at 2:11
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    $\begingroup$ @MikeDunlavey The line is however wide standard lines on a road are (about 10cm?); I'm riding at 10-15mph. You were talking about lines on a road so I'm not sure what is the relevance of cycling down a 1cm-wide, 100m-long rail. It's as if I've said that walking along a line on the road isn't hard and you suddenly switch to tight-rope walking. $\endgroup$ – David Richerby May 22 '16 at 2:16
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    $\begingroup$ @MikeDunlavey yup, there's a video: redbullchannels.pmd.redbull.com/hds/1439051358001/201509/3780/… (skip to 2:40). It's also been (kind of) done by a bear, because Internet: youtube.com/watch?v=owKQL4JY3UU $\endgroup$ – Dave May 22 '16 at 21:00
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By the principle of relativity, you will not fall over – assuming that you know how to use the bike and you won't be deliberately "confused".

The principle says that the laws of physics have the same form in all inertial frames that are moving by a constant velocity relatively to each other. The reference frame associated with the moving sidewalk is as good as the reference frame associated with the static sidewalk. In both cases, the bike is moving relatively to it, so if it can stand and move in one situation, it will stand and survive in the other, too.

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    $\begingroup$ The only difference between the two cases is the wind. At bike speeds aerodynamic effects are not that important. $\endgroup$ – Andrea May 21 '16 at 19:00
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    $\begingroup$ @AndreaDiBiagio Well, aerodynamic effects are pretty significant to cyclists: for example, drafting behind another cyclist requires about 30% less power than cycling on your own. But I agree that they're not significant to the question of whether or not you'd fall off. $\endgroup$ – David Richerby May 21 '16 at 19:25
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    $\begingroup$ Dear @SergeBorsch, what solves the "problem" of spinning is not our getting used to it but the equivalence principle: the centrifugal force from the spin (non-inertiality) acts as indistinguishable outward gravity whose acceleration is between 0 and 0.03 meters per squared second, depending on the latitude, so it cancels 0-3 percent of the Earth's gravity. We always face gravity on the Earth's surface - what we normally count as gravity is up to 3% different than what is "gravity from Earth's mass", the small fraction is from the non-inertial motion $\endgroup$ – Luboš Motl May 22 '16 at 4:19
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    $\begingroup$ The shortest answer to these sorts of questions is: the Earth is moving! Will a treadmill really make much difference to your "absolute velocity" (not that there is such a thing) $\endgroup$ – Robin Hartland May 22 '16 at 18:59
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    $\begingroup$ @RobinHartland , I agree it's the pedagogic way to argue that the moving doesn't matter. Still, people may develop all kinds of irrational reasons to think that the moving and spinning Earth doesn't matter while the moving sidewalk would matter, that the motion relatively to the Earth is absolute. $\endgroup$ – Luboš Motl May 23 '16 at 5:03
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Yes: I've done that. I used to have a device for the purpose, commonly called "rollers". It's like a treadmill for bicycles.

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I would say it is the tire deformation keeps up the bike rather than unconscious steering tweaking; at high speed, high frequency tweaking is impossible.

Imagine or if you see the cross section of a tire, you can see it is least deformed when the portion is not close to the ground. And it is flattening deformed when it is in contact with ground. The deformation needs force and produce force. There are many factors. But the high the rotating speed, the high the force (due to smaller delta time). The upward force counter-react to any gravity center side shifting and stabilize the bike.

So whether you ride on moving side walk or anywhere, in order to get you stay up, you need let the wheel spin fast on the surface.

Sometimes, I was wondering what if a bike doesn't have a rubber tire.

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    $\begingroup$ Tire deformation isn't critical to the bike staying upright. Test your theory on a BSO with the tires taken off and you'll see you can stay upright just fine. Penny farthings had solid wheels. $\endgroup$ – whatsisname May 22 '16 at 6:27
  • $\begingroup$ Talking about Penny Farthings, it is true having solid wheels but that is rubber solid wheels. This clears my puzzle that even with wood tire, it is still elastic material and can produce force though more rigid and thus less stable. $\endgroup$ – user115350 May 22 '16 at 15:00
  • $\begingroup$ For those who aren't regulars at bicycles.se, @whatsisname was referring to a "bicycle shaped object". And a completely flat tyre can be ridden on, taking next to no force to deform it (not recommended). $\endgroup$ – Chris H May 23 '16 at 8:17
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Roughly speaking, a bike doesn't tip over because as soon as you start to tip over, gyroscopic effects (those weird forces you feel when you try to rotate a fast spinning object) together with the structure of the bike cause it steer towards the direction of tipping. Turning in the direction of tipping causes a centrifugal force which will turn the bike upright again (stopping the steering).
A well-built bike will increase the stability as well as a human riding the bike, because it can supply arbitrary forces to balance the bike. (well trained people could balance a bike that isn't moving)

The gyroscopic effects don't require any motion and the centrifugal force only requires that the ground is moving relative to the bike. So yes, it is possible provided that the sidewalk is moving with enough speed. Anyone willing to try at the airport?

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    $\begingroup$ Bike stability has little to do with gyroscopic effects. Somebody built a bike with an extra wheel mounted by the road wheels and geared so it spins at the same speed but in the opposite direction, almost entirely cancelling out the gyro forces. ("Almost" because the wheels weren't exactly co-axial.) It was just as easy to ride as any other bike. $\endgroup$ – David Richerby May 21 '16 at 19:29
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    $\begingroup$ @DavidRicherby interesting! Do you have a link? $\endgroup$ – DilithiumMatrix May 21 '16 at 23:42
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    $\begingroup$ Gyroscopic effects have been disproven to cause a bike to stay up. todayifoundout.com/index.php/2011/12/… And here's the empirical test www2.eng.cam.ac.uk/~hemh/gyrobike.htm where a counter-rotating wheel was rigged. $\endgroup$ – Criggie May 22 '16 at 0:08
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    $\begingroup$ To elaborate on this answer, countersteering is what makes a bike stay upright: bicycles.stackexchange.com/a/5341/683 $\endgroup$ – whatsisname May 22 '16 at 2:46

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