# Settle this Disagreement? Concerning Conservation of Angular Momentum

• nonequilibrium
In summary, the teacher's first explanation for a wheelie is that it is due to the torque exerted on the bike by the ground and the rider's weight.

#### nonequilibrium

[settled] Settle this Disagreement? Concerning Conservation of Angular Momentum

[settled] Hello,

In my Classical Mechanics exercise session we had an exercise with a bike rolling without slipping. You had the calculate the acceleration at which the bike's front wheel would lift off from the ground (and there was a motor on the rear wheel).

I had a disagreement with the assistent regarding the physical origin of this effect (or rather, the principle cause). According to him it was due to friction (some weird coupling of friction that happened to result into this), while I claimed it was a direct cause of conservation of angular momentum.

First I claimed the same effect would also happen with a motorcycle on ice, with which he disagreed. He claimed that the change of angular momentum in the rear wheel was being balanced by a change of angular momentum in the motor attached to the wheel, so that conservation of angular momentum would not manifest itself in turning the frame of the motorbike. Eventually I seemed to have convinced him of my point (by for example replacing the engine with a human -on the bike seat- turning the rear wheel himself) and he agreed it would happen on ice, but he said they were very different situations in the sense that in the second case it is the manifestation of another effect, one not responsible for the first case.

For the purist it might seem non-sensical to argue about the physical origin of this, since I suppose in a sense there is no clear distinction between "it's the friction" or "it's the conservation of angular momentum", because everything, in the end, is nothing more and nothing less than the three laws of Newton, but I think that if you take it a bit more informal it is okay to talk about the principle explanation for the effect, and I think it's clear there's a clear distinction between my views and those of the assistant (and also a promimenent student of the class agreed with the assistant, which made me less certain of my claim, but I still see more logic in my reasoning than his).

What do you think? Isn't it just conservation of angular momentum that makes the frame of the bike tilt up when I accelerate my rear wheel?

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Angular momentum of motor and tire are only conserved in the frictionless case. If there's friction between tire and road, then the momentum effect on Earth needs to be taken into account, and then angular momentum of engine, tire, and Earth are preserved.

A wheelie occurs when the torque due to the forward force at the pavement and the backwards reaction force at the center of mass is greater than the opposing force due to gravity pulling down at the center of mass and the pavement pushing up at the contact patch of the rear tire.

When motocross motorcycles do large jumps, and while in free fall, then accelerating or braking the rear wheel can be used to adjust the "pitch" of the motorcycle, but it's not enough of an effect to cause a wheelie that opposes the torque related to gravity.

I removed my post as rcgldr put it so much better than me.

Knew what I was trying to say, just couldn't get the words out. :tongue2:

I will add though, on a frictionless surface (your example ice), you won't do a wheelie.

This has nothing to do with conservation of angular momentum.

Your teacher's first explanation was probably correct (though you didn't explain it very clearly in your OP). The horizontal force which accelerates the bike is the friction force between the rear wheel and the ground. However the center of mass of the bike and rider is some distance above the ground. So relative to the center of mass, the rear wheel is providing not only a force, but also a moment that is trying to turn the bike and lift the front wheel.

If the acceleration is small, this turning moment is balanced by an equal and opposite moment, caused by the fact that the weight of the bike shifts to be greater on the rear wheel than the front wheel. When the acceleration is big enough, the weight on the front wheel reduces to zero and the bike starts to do a wheelie.

You can show the same effect on an object with no wheels and no rotating motor, and therefore no angular momentum to conserve. Get a rigid box, or a block of wood, and stand it on a table with the longest side vertical. Push the box at the base, to correspond to the friction force acting on the bike at road level. If you push gently, the box will slide along the table without falling over. If you push hard, the front edge will lift off the table and it will fall over "backwards". With a bit of practice you might be able to push it along doing a "wheelie", with only the back edge on the table.

Oh okay, I had wrongly assumed that a mid-air wheelie had the same underlying principle as in the exercise in question. The assistant was wrong on denying that a motor cycle wouldn't flip over if you give gas hanging somewhere in interstellar vacuum, but he was right on the more important part that (once he seemed to be convinced of the former being possible) that they had different principle causes, which you guys now explained, thank you.

mr.vodka,

Without doing any calculations, or giving the problem considerable thought, my initial instinct is that friction is the primary cause. If not, then the same bike in space would "pop a wheelie" when you pedaled it; and if that were the case, a precession drive would work, and FTL would be possible. Since FTL is not possible, I must assume the answer is friction ;-)

Fish

Wait, a bike wouldn't pop a wheelie in outer space?

mr. vodka said:
Wait, a bike wouldn't pop a wheelie in outer space?

Well the wheel would spin in one direction and the bike would spin in the opposite direction.

So yes, it would pop a wheelie, I think Fish4Fun thought of the bike "popping a wheelie" and the wheel not turning - indicating some magic friction force holding it in place.

Oh okay ;)

## 1. What is the conservation of angular momentum?

The conservation of angular momentum is a fundamental principle in physics that states that the total angular momentum of a closed system remains constant over time. In other words, the total amount of rotational motion in a system does not change unless an external torque is applied.

## 2. How does the conservation of angular momentum apply to objects in motion?

The conservation of angular momentum applies to all objects in motion, whether they are rotating or moving in a straight line. This is because angular momentum takes into account both the mass and velocity of an object, as well as its distance from the axis of rotation.

## 3. Can angular momentum be transferred from one object to another?

Yes, angular momentum can be transferred from one object to another through collisions or interactions between the objects. However, the total amount of angular momentum in the system will remain constant.

## 4. How does angular momentum affect the motion of objects?

Angular momentum affects the motion of objects by determining how they rotate or spin. Objects with a higher angular momentum will have a greater tendency to resist changes in their rotation, while objects with a lower angular momentum will be easier to rotate or change their direction of rotation.

## 5. What are some real-world applications of the conservation of angular momentum?

The conservation of angular momentum has many real-world applications, including the motion of celestial bodies such as planets and stars, the movement of satellites and spacecraft, and the operation of gyroscopes and spinning tops. It is also important in understanding the stability of structures such as bridges and buildings.