# Man on a bike - leans into a corner. How?

1. Dec 7, 2008

### Debozo

OK, a Man on a bike - leans into a corner to make a turn. How does he do that?

Don't the laws of physics say that it's impossible for him to shift his center of mass from side to side? There's nothing for him to push against (side to side)

It's like being up in space. and he shouldn't be able to shift the center of mass, no matter how hard he tries it.

If he leans to the right, the bike will lean to the left to compensate, and he can't get round the corner because he simply can't shift the center of mass. (Or so say the laws of motion)

Well, we all know it IS possible to ride a bike around a corner, So what's going on ?

2. Dec 7, 2008

### nealh149

It's not a closed system. The bike pushes on the ground.

3. Dec 7, 2008

### Staff: Mentor

Also, even if it were a closed system, (e.g. a man on a bike falling through vacuum) the man would still be able to shift the position of the wheels wrt his center of gravity.

4. Dec 7, 2008

### Debozo

No it can't.

The bike can not push on the ground until the man has shifted his mass from left to right.
And the laws of motion say that it's not possible to shift your centre of mass unless you have something to push against.

5. Dec 7, 2008

### Debozo

If he moved the position of the wheels wrt the center of gravity some other mass would move to compensate - other wise the laws of physics are wrong

I think the laws say you can't move your center of mass if you cant push against something

6. Dec 7, 2008

### turbo

Ever hear of counter-steering?

7. Dec 7, 2008

### Staff: Mentor

Not to be rude, but you might spend a little more effort trying to understand the correct responses that you got or asking for clarification rather than telling people that they are wrong when they are not.

The point is that he does have something to push against. The ground. The laws of motion that you are refering to say that the total momentum (center of mass) of an isolated system is constant. The man on the bike does not form an isolated system.

The point is that you don't have to move your center of mass in order to move the wheels relative to the center of mass.

Although this isn't an isolated system it may be easier for you to visualize: Let's say that the man and the bike are suspended from a string. If he pulls the bike to the right then the rest of him will go to the left, he hasn't changed the position of the center of mass, but he has changed the position of the wheels wrt it without pushing on anything external.

Last edited: Dec 7, 2008
8. Dec 7, 2008

### rcgldr

The OP never mentioned closed system. My guess is that what he's thinking about is the fact that a bicycle is a uni-track vehicle as opposed to a closed system, and a bicycle would provide little inertial resitance (linear or angular) to weight shifting by a rider realtively high above the ground where the torque force would be high compared to the bicycles angular inertia. If the weight shifting was done close to the ground, then the torque force would be relatively small compared to the angular inertia of the bicycle and the center of mass could be accelerated sideways, although the end result would be an unbalanced system.

A rider could generate a torque by leaning, which will be opposed by the ground via a horizontal force. However the force would be small, and the only time I've seen torque used for balancing while still is circus type hi-wire acts with a bicycle on a wire and the rider creating torque via arm movments, or by using a long balance pole.

Standing still, note that the steering geometry at the front tire causes the contact patch to move side to side, because the contact patch is "behind" the pivot axis line for steering. Steer left, and the contact patch moves right, and the ground reacts with a leftwards force, so the correction response while standing still is the normal one used while riding, but very small. Veledrome bicycle racers can stand still indefinately using this method, part of a waiting game some riders do at the start of a race.

If the bicycle is moving, then balance is maintained via counter-steering. The steering geometry again contributes to self stability once above a certain speed. If the bicycle leans, the front tire is turned inwards enough to cause the bicycle to straighten up. If the rider isn't directly counter-steering, then the rider may be indirectly counter-steering by leaning, which causes the bicycle to lean the other way, which results in the front tire turning "outwards" because of the steering geometry. At this point the center of mass is offset, and the bicycle continues to lean inwards until the steering geometry or rider corrects the situation (or the bicycle just falls over).

9. Dec 7, 2008

### Staff: Mentor

An isolated system (no external forces) is the only kind of system where "you can't shift the center of mass".

10. Dec 8, 2008

### Debozo

Finally. Somebody with what looks like a sensible answer. Cheers Jeff. Something to think about. I think you've probably cracked it. The higher the rider is, the harder it is for him/her to push against the ground. Probably true.

But I don't understand why there's this obsession with defining whether its a closed system.
There's really no such thing as a closed or an unclosed system is there. If an object appears to be able to move its center of mass then it has really pushed against another object and the other object moved the other way. Most likely a heavier one, and we're usually thinking about our planet - pretending it stands still when we move around. If you move to the left, the ground beneath you moves to the right. The planet rotates to compensate, otherwise the laws of physics would be wrong.

Arguing about closed system or not, seems to me to be a worthless concern. Trying to simplify things so that you can talk about moving a centre of mass around by exerting forces - that just makes it more confusing in a way, and you have to distort the laws of motion as a result - adding the caveat about closed system as a result. I don't see the point of it really. Anyway...

I think I'm right in thinking that the laws of motion are actually saying you can't move the centre of mass, ever. It's kinda odd. I think it applies with quantum physics and relativity too - since light is a carrier of mass.

Wow, learning to ride a bike is hard. ;-)

11. Dec 8, 2008

### Debozo

No. It's not possiblle to ever shift the center of mass of any system.

If an outside object exerts a force (your external force) then that outside object is by definition a part of the system.

And the center of mass of the system stays just were it always was. - until yet some other object hits (or exerts a force through some field). And it too becomes a part of the system. And on.. and on..

Being able to move the centre of mass is a pretence.

12. Dec 8, 2008

### turbo

I asked if you had ever hear of countersteering, hoping that you might seek some references, instead of repeating that a biker cannot move his center of mass. Here is a Wiki page. I would prefer not to reference Wiki, but this happens to be a good page, and well-supplied with references. A biker can and does move his center of mass by countersteering, then maintains the lean angle with positive steering, then exits the curve (straightens up, putting his center of gravity over the wheels) with another countersteering maneuver. The contact patch of the tires allows the riders to control their lean angle (center of gravity) with very little mechanical input.

http://en.wikipedia.org/wiki/Countersteering

13. Dec 8, 2008

### Math Jeans

You do realize that space is not a perfect vacuum and there is a minimal resistance force inside of it that does allow for small changes in center of mass.

14. Dec 8, 2008

### Staff: Mentor

No, this is completely incorrect. You can always completely arbitrarily define your system to be whatever you wish, even chopping an object in two if you are interested in calculating internal stresses etc. If you had ever done free-body diagrams you would understand that isolated systems are, by far, the exception, and certainly not the rule.

The statement that the center of mass does not move is only true for an isolated system, and even then it is only true in the center of momentum frame (where its truth is a tautology).

15. Dec 9, 2008

### Debozo

If you use friction/air resistance or whatever to move around (to push against), then you move the planet earth in the opposite direction. You are on a space-station. A big one.

You are stuck on a planet floating in space. But it's not rigidly attached to anything, its just floating like a giant space-station. Nothing in this universe is anchored in space. And that's precisely what the laws of motion are all about.

Last edited: Dec 9, 2008
16. Dec 9, 2008

### Debozo

Wrong. Every system (ultimately) is isolated, because ultimately everything is floating in space, just like an astronaut does. In fact if you assume your reference frame is fixed you are contradicting the laws of motion (aka the conservation of momentum).

The only system that isn't isolated is one fixed in space because it has infinite mass. There is no such thing.

Sure you can, but then your reference frame isn't an inertial reference frame is it. It's only an approxiamation of one ,and if its mass is very small compared to the object it exerts a force on then it's not even close to inertial. Using an accelerated frame as reference and thus pretending that it isn't moving/accelerating is supposed to be bad practice in physics. So what's goin on.

17. Dec 9, 2008

### Cthugha

Ouch. That momentum (or some other quantity - depending on your kind of system) is not conserved inside an open system is not contradicting the laws of motion. It is an important part of the definition of an open system. You are just using your own definitions at the moment, which are different from the ones used in physics.

There is only one single system, which is truly isolated: the universe as a whole.

Completely wrong. You do not need an accelerated frame to describe external forces. You just need to know, that conservation rules do not necessarily apply to open systems and this makes complete sense: why should anyone bother about constructing some strange pseudoclosed system, which is not in equilibrium, if only the physics inside a single subsystem of this whole nonequilibrium system is of interest? Please don't tell me, you would really model a boiling put by calculating the change of pressure in the universe when some water evaporates.

Remember that guy is not just a point of mass, so he can easily push against something side to side. If he was a point on line, he would be in trouble.

Last edited: Dec 9, 2008
18. Dec 9, 2008

### D H

Staff Emeritus
No, you are the one who is wrong. Drawing a system boundary is a bit of an art. Do it wrong and you get a system that doesn't readily answer the question at hand or is very hard to model. Do it right and you can answer the question at hand -- in this case, "OK, a Man on a bike - leans into a corner to make a turn. How does he do that?"

Physicists and engineers wouldn't use terms like non-isolated system, external force, external torque, etc., if every system was isolated. Ultimately, the only isolated system is the universe as a whole. I do not need to model the myriad interactions among the remote stars to understand why this is possible:

19. Dec 9, 2008

### Staff: Mentor

It is pretty clear that you have little or no experience actually drawing free-body diagrams and working physics problems. Because of this you have some fundamental misunderstandings relating to standard physics terminology and basic mechanics concepts.

While there is nothing wrong with ignorance, it is rather arrogant of you, from your ignorance, to presume to be qualified to correct the PhD-level physicists and engineers that populate this board. Your ignorance can be fixed, but only if you discard your arrogance first. You have already been corrected multiple times by multiple people and it is up to you to decide if you want to learn or not.

If this sounds dismissive it is, I have enormous respect and patience for students struggling to master difficult concepts, but no respect for people who think that their ignorant thoughts and lazy opinions have some intrinsic merit simply because they state them.

20. Dec 9, 2008

### turbo

You are making this far more complicated than it is, and then trying to derive a general rule from a system that you have improperly defined. That's what's going on. Look at the picture of the motorcycle racer that DH posted. His front tire is turned in the direction of his turn and he is leaning INTO the turn with his body weight helping him maintain the angle through the turn.

He initiated the turn by counter-steering at the end of the straightaway, which threw his center of gravity to the right, then as he got to the right turn angle, he steered to the right. Steering hard toward the right while applying throttle helps the rider get through a tight right turn at higher speed, BUT it also exerts a force that wants to force the bike upright, so the rider shifts his body-weight to the inside of the turn to counteract that. If he did not shift his weight, the bike would tend to right itself due do the hard steering, and he would drive off the outside of the curve.

There is nothing mysterious about the physics of riding bicycles or motorcycles. Calculating all the forces involved is a complex job, but the physics is well-understood.

21. Dec 9, 2008

### Debozo

amusing.

Ok guys and girls . It's obvious you can't debate the simplest laws of motion without attempting to get get into a kinda amusing condescending personal attack. If what I've said is so obviously wrong, then it should be easy for you to explain why. Nobody here has done so. Nobody here has yet said anything I didn't already know. That's why I don't have any reason to change my opinion.

By resorting to personnal attack you've give the impression you can't answer me. Because you yourselves just don't know the answer, maybe that's it - I'm not sure.

As far as I can see the laws of motion state that it's impossible to move the centre of mass of any object. If you push on something you imediately move in the opposite direction. And Lo and behold the centre of mass of yourself and that object stays put. Stating you CAN move the centre of mass is only an approximation where for example you're attached to a large object like the Earth. Fact.

If anybody here can prove that's wrong i'd like to see it. That's the only reason I posted it here. To debate whether it's true or not. Chanting "you're an idiot, and I've got some qualifactions" is a very weak answer IMHO. :-)
If you 've got some qualification then use them to explain why it's wrong (it isn't).

Dale, I don't think what you said earlier is true actually. If you take any lightweight object as the rest frame and pretend it doesn't accelerate (AKA move), the maths may work out fine, but you then have to explain why the rest of the universe starts accelerating past it. So I don't think it would work, moving the entire universe takes a lot of energy...

22. Dec 9, 2008

### Debozo

turbo, I think maybe you haven't undestood the question

the question is how can any object that isn't firmly anchored to the ground shift it's centre of gravity.

The answer is that it can't. If he moves his mass to the right the bike will move to the left. The centre of gravity would stay fixed. So he can't lean into the corner.

Jeff's answer got closest by noting that the tire contact patch is fixed (pretty much in simple analysis), and thus can be used with the inertial mass of the bike+rider to exert a sideways force/or torque on the ground. [which you can assume is fixed if you wish - I'm not fussy]

23. Dec 9, 2008

### Cthugha

The answer has been given to you many times. You have wrong ideas and use extremely sloppy (and sometimes wrong) vocabulary.

Of course. But you are one object. You and that thing you push on is a different object. Your center of mass moves. The center of mass of the other object moves. The combined center of mass of you and the object you pushed does not move. So it is already obvious that your statement "it's impossible to move the centre of mass of ANY object" must be wrong. Redefining your objects any time you like does not work. All of these three are objects. That you can always find a system, where the center of mass does not move is trivial, but does not tell us anything about the single objects.

No. You are just defining, that the only valid objects are those, which cannot change their center of mass. This definition is just arbitrary and just not the definition all other people use. I can also show, that pigs can fly, if I define, that anything with wings is a pig.

24. Dec 9, 2008

### turbo

The bike IS attached via gravity and coupled to the ground via frictional forces. By leveraging the steering geometry of the bike, the rider can very easily change his center of gravity. There is no mystery.

A vehicle balanced on two wheels is inherently unstable, and it is this inherent instability that makes it so easy for the rider to change his center of gravity and negotiate turns. Such a vehicle that is NOT in motion will fall over if not propped up. Sit on a bike without moving. How long can you do that before your center of gravity changes in a very sudden and perhaps painful way?

Nobody here is making personal attacks or taking pot-shots at you. You have gotten some very good answers from the standpoints of both engineering and physical systems.

25. Dec 9, 2008

### Debozo

I don't think so. It's the basis of the laws of motion if you think about it

Sorry I haven't a clue what you're on about.
All I've said is that when something moves it has to move another object in the opposite direction to keep the centre of mass fixed. And there's no way around that. I haven't defined anything.