Bicycle Questions: Static Friction & Gear Ratios

[mattt]

Anyway, the example of one single wheel rolling on an horizontal ground is even more interesting.

I guess you are perplexed that if the wheel is rolling (without sliding) and the only exterior forces acting on the wheel are the weight, the normal force and the static friction force, how is it that the wheel end up stopping if the only force that causes a non-zero torque (wrt COM) is the static friction force and it "should" increase the angular velocity (the angular momentum vector) ? :-)

Or imagine you are pushing the center of mass of the wheel so that the center of mass is moving with uniform rectilinear motion. Again, the only force (apparently) that causes a non-zero torque (wrt COM ) is the static friction force and, again, it "should" increase the angular velocity (angular momentum vector), how is it that the angular velocity remains constant? :-)

As I said, this example is good enough to test many things about Newtonian mechanics. I'll leave it to you to think about it and later on I'll comment on this example. :-)

 

[A.T.]

you have to explain better how the friction which is applied at the contact point in the ground, transforms the work of the force from the fork to the axle into rotational kinetic energy.

When you push a standing person at his center of mass, the friction at his shoes transforms the work you do into rotational kinetic energy. Do you understand that?

What i see is that the torque of friction...

You confuse reference frames. In the ground frame the instantanious center of rotation is the point where the friction acts, so it creates no torque around that point.

 

[Delta2]

When you push a standing person at his center of mass, the friction at his shoes transforms the work you do into rotational kinetic energy. Do you understand that?

No. What is the definition of "Force A transforms the work of Force B" there is no such definition in physics. There is Force A does work, or Force A creates Torque, or Force B gives impulse.

You confuse reference frames. In the ground frame the instantanious center of rotation is the point where the friction acts, so it creates no torque around that point.

i can choose whatever frame i want and a constant point in the frame to take the torques of the forces.

 

[Delta2]

Yes.


As you can see in this last example, that is not true. :-)

yes ok it might not be true in ur example but it still hold in the case of our interest with the bike.

 

[rcgldr]

The issue here is that rolling involves surfaces that move with respect to each other. Any point on the wheel is moving in a cycloid path, and over the period of time for each revolution of a wheel, the average velocity of any point on the wheel relative to the ground is the same as the average velocity of the bike relative to the ground.

There's no claim the ground is performing work (assuming a ground based frame of reference), it's the internal energy source that is doing the work, exerting a backwards force onto the ground, and with the Newton third law reaction of the ground exerting an equal but opposing forwards force onto the wheel. Here's a link to a web article about this:

http://electron6.phys.utk.edu/101/CH2/wheels.htm

Another example of this would be a solid uniform sphere rolling up or down an incline without slipping. The total change in energy of the ball equals m g Δh, composed of linear and angular energy. The change in the angular component of energy is due to the static friction force exerted by the incline onto the ball opposing the gravitational component of force, and equals the static friction force times the distance rolled. Similar to above, there's no claim that the incline is performing work, in this case gravity is responsible for the change in energy.

Yet another example would be a solid uniform sphere rolling on the accelerating surface of a very long treadmill. In this case, the treadmill is the source of energy. The center of mass of the sphere will accelerate at 2/7th's the rate of acceleration of the tread mill, relative to the non-moving ground. The static friction force times the distance moved relative to the non-moving ground will equal the change in linear kinetic energy of the sphere (relative to the ground). The static friction force times the sphere surface distance rolled (or torque times angular displacement) will equal the change in angular kinetic energy of the sphere.

 

[Delta2]

The issue here is that rolling involves surfaces that move with respect to each other. Any point on the wheel is moving in a cycloid path, and over the period of time for each revolution of a wheel, the average velocity of any point on the wheel relative to the ground is the same as the average velocity of the bike relative to the ground.

Ok, but sorry what is the point of this point?

There's no claim the ground is performing work (assuming a ground based frame of reference), it's the internal energy source that is doing the work, exerting a backwards force onto the ground, and with the Newton third law reaction of the ground exerting an equal but opposing forwards force onto the wheel. Here's a link to a web article about this:

http://electron6.phys.utk.edu/101/CH2/wheels.htm

Ok fine ground does not perform work. The internal energy is doing work and is keeping the friction force alive (thats what you saying if i understand correctly). Does the friction force gives impulse or the impulse is zero also? And if the impulse is zero how the momentum of the bike is changing?
Also in the link you gave when it says "Sliding friction converts (or transforms) most of the work you do on the file cabinet into thermal energy" it admits that the sliding friction does work. Anyway that's for sliding friction. What the interesting portion for me in this link is :

"##How can the force of static friction be responsible for accelerating the car and do no work? Internal forces between different parts of the car in the engine, transmission, etc, come in action-reaction pairs. These forces can do work. The frictional force can cancel one of the forces of an action-reaction pair with a direction opposite to the direction of the acceleration, leaving a net force in the direction of the acceleration."

Ok fine friction cancels one of the forces in an action-reaction pair, but how it cancels the work of that internal force, since the friction doesn't do work?

Another example of this would be a solid uniform sphere rolling up or down an incline without slipping. The total change in energy of the ball equals m g Δh, composed of linear and angular energy. The change in the angular component of energy is due to the static friction force exerted by the incline onto the ball opposing the gravitational component of force, and equals the static friction force times the distance rolled. Similar to above, there's no claim that the incline is performing work, in this case gravity is responsible for the change in energy.

Yet another example would be a solid uniform sphere rolling on the accelerating surface of a very long treadmill. In this case, the treadmill is the source of energy. The center of mass of the sphere will accelerate at 2/7th's the rate of acceleration of the tread mill, relative to the non-moving ground. The static friction force times the distance moved relative to the non-moving ground will equal the change in linear kinetic energy of the sphere (relative to the ground). The static friction force times the sphere surface distance rolled (or torque times angular displacement) will equal the change in angular kinetic energy of the sphere.

So though again the friction does no work you saying that the changes in energy equal to some sort of "pseudo work" of friction right?

 

[A.T.]

No. What is the definition of "Force A transforms the work of Force B" there is no such definition in physics. There is Force A does work, or Force A creates Torque, or Force B gives impulse..

When you push someone over, the friction at his feet acts as a constraint which enforces a certain movement (rotation), but does no work on him in the rest frame of the ground. Do you understand that?

i can choose whatever frame...

The rule that static friction does no work applies in the rest frame of the contact surfaces. In other frames it can do work.

 

[rcgldr]

Does the friction force gives impulse

Yes. It doesn't matter that the ground is not the source of energy when the ground exerts a forwards force in reaction to the wheel exerting a backwards force. The net impulse on the bike will be the forwards friction force x time and the net change in energy of the bike will be the forwards friction force x distance traveled relative to the ground (well almost, a tiny amount of the energy change goes into the earth).

Ok fine friction cancels one of the forces in an action-reaction pair, but how it cancels the work of that internal force, since the friction doesn't do work?

The friction doesn't cancel one of the forces. The backwards force exerted by the wheel onto the ground affects the earth. The forwards force exerted by the ground onto the wheel affects the bike. The change in momentum of Earth and bike cancel each other, since the Earth and bike can be considered a closed system with no external forces. Almost all of the change in energy goes into the bike since the Earth is so massive that the change in momentum (equal and opposite of that of the bike) results in a very tiny change in speed.

The rule that static friction does no work applies in the rest frame of the contact surfaces. In other frames it can do work.

Rolling motion complicates this. In the rest frame of the ground, the average velocity of any point on the surface of the wheel during the time it takes to make some integer number of revolutions is the same as the average velocity of the bike during that time period.

 

[Delta2]

Ok guys let me get this straight.

Total translational KE changes (in some cases) as the result of the work of only internal forces, however total linear momentum changes only by the impulse of external forces (impulse doesn't have work as consequence necessarily).

I have to say the more i think of this the more weird and strange it looks to me. I don't know why.

 

[Delta2]

The friction doesn't cancel one of the forces. The backwards force exerted by the wheel onto the ground affects the earth. The forwards force exerted by the ground onto the wheel affects the bike. The change in momentum of Earth and bike cancel each other, since the Earth and bike can be considered a closed system with no external forces. Almost all of the change in energy goes into the bike since the Earth is so massive that the change in momentum (equal and opposite of that of the bike) results in a very tiny change in speed.

But that's what it says at the link. The way you describe it now makes it look to me like the friction(force from ground to the wheel) changes the energy of the bike. Ok hm i guess the friction redirects most of the energy back to the bike via its impulse not work. (Problem here is that there is not official definition of a force that redirects or transforms work or energy but oh well wth)

 

[rcgldr]

But that's what it says at the link.

Now that I've read the article linked to before, it's worded awkwardly. Newton third law pair of forces do not act on the same object, so they don't "cancel". In this case, the third law pair of forces is the backwards force that acts upon the surface of the Earth (exerted by the wheel) and the forward force that acts upon the wheel (exerted by the surface of the earth). The article is either treating the Earth as if it had infinite mass, resulting in a force that is "canceled" because it's acting upon an object of infinite mass and has zero effect on the earth, or it's just ignoring the effect on the earth, so it's not a closed system where momentum of the system would be conserved.

The way you describe it now makes it look to me like the friction(force from ground to the wheel) changes the energy of the bike.

The origin of the friction force is the torque that the rider exerts onto the pedals. The momentum of Earth and bike are changed with equal magnitude but opposite direction. The energy of both Earth and bike are changed, but as mentioned before, since the Earth is massive compared to the bike, the velocity change of the Earth is tiny compared to the velocity change of the bike, so the bike gets most of the change in energy.

 

[A.T.]

Problem here is that there is not official definition of a force that redirects or transforms work or energy but oh well wth

There is an official definition of work. And forces that do no work are usually called "constraint forces".