How does friction affect the acceleration of a rolling wheel?

[Poligon]

Hi everyone, Good day.
for the effect of friction on wheel (all the questions are based on rolling without sliding), i know that in the case of uniform rolling, there will be no friction on the wheel. while for accelerating or decelerating case, there will be friction on the wheel (but in certain circumstances, depends on the mass moment of inertia of the wheel, the friction can be zero).
the first question is, when uniform rolling is achieved on a frictionless surface, what will happen?
1. the car will stay on the same spot with the wheel keep rolling? or
2. the car will continue to move forward with the wheel keep rolling? or
3. the car will continue to move forward with the wheel sliding?
the second question is, in the case of accelerating or decelerating, does the friction act on the wheel causes loss? i mean does this friction affect fuel efficiency?
the third question is, looking at the attachment, it is found that if r1 = 0.5r2, then the friction force will be zero, if r1 > 0.5r2, the friction is in the direction as drawn in fbd, if r1 < 0.5r2, the friction is opposite to the direction as drawn. what does zero friction indicates? why zero friction still allows the wheel to accelerate? other than that, what does different friction direction indicate?

 

[jedishrfu]

This looks like a homework assignment. We need to see your work before we can help.

So what do you will happen with a car on a frictionless surface trying to move forward?

 

[Poligon]

Nope, this is not a homework assignment. i want to know this because i am joining a competition, which involving building a fuel efficient car. I attached my fbd and calculation with the post, can you see it?
since uniform rolling does not have friction acting on the wheel, i think maybe it will rolling with the car moving forward?

 

[jack action]

Hi everyone, Good day.
for the effect of friction on wheel (all the questions are based on rolling without sliding), i know that in the case of uniform rolling, there will be no friction on the wheel. while for accelerating or decelerating case, there will be friction on the wheel (but in certain circumstances, depends on the mass moment of inertia of the wheel, the friction can be zero).

If you refer to a powered wheel on a car, the sentence in bold is not true. The friction is not a reaction to the acceleration, it is the acceleration that is a reaction to the friction. The torque of the wheel (produced by the engine) will create the friction force, which in turn will accelerate the wheel (and the car). The mass moment of inertia may reduce the acceleration, but never sets it to zero because, in this case, ma (combined with I alpha of the rotating parts) is the equal and opposite reaction to the friction force (assuming no drag or rolling resistance).

the first question is, when uniform rolling is achieved on a frictionless surface, what will happen?
1. the car will stay on the same spot with the wheel keep rolling? or
2. the car will continue to move forward with the wheel keep rolling? or
3. the car will continue to move forward with the wheel sliding?

#2. With uniform rolling, when the car hits the frictionless surface, it is like if there was suddenly no ground under the car, so it will continue to go forward at constant speed and the wheel will continue rotating at the same constant angular velocity.

the second question is, in the case of accelerating or decelerating, does the friction act on the wheel causes loss? i mean does this friction affect fuel efficiency?

Yes and no. Friction by itself does not cause losses, but friction cannot exist without slip. Slip will create energy loss in form of heat. You can have the exact same friction force acting on the wheel but two different values of slip.

the third question is, looking at the attachment, it is found that if r1 = 0.5r2, then the friction force will be zero, if r1 > 0.5r2, the friction is in the direction as drawn in fbd, if r1 < 0.5r2, the friction is opposite to the direction as drawn. what does zero friction indicates? why zero friction still allows the wheel to accelerate? other than that, what does different friction direction indicate?

Your question comes from the fact that you are mixing 2 types of problem together. The problem you present here is for a rope that pulls a spool. You are looking for answers for a wheel driven by a torque.

In the problem presented, the pulling force creates the friction and the acceleration, one can exist without the other as even if the friction is not present, the rope will still pull the spool.

On a car, the torque creates the friction, the friction creates the acceleration. There are no other linear force acting on the car. If the friction is not present, there will be no acceleration.

So, in you attached calculations, there shouldn't be a force F, but a torque T instead. Your equations become:

f = ma
T - f r₂ = I alpha

or:

f = (T - I alpha) / r₂

or:

T = ma r₂ + I alpha

and since a = alpha r₂:

T = ( mr₂² + I ) alpha

 

[Poligon]

I think I can understand now. Thanks a lot!
If it is really a spool pulled by a rope, for r1 > 0.5r2, the spool will roll, while for r1 < 0.5r2, the spool will slide right?
One last question will be, can you explain why for a front wheel drive, there is no friction acted on rear wheel? How to come to this conclusion?
I cannot understand this because the explanation i can think of is the engine will provide torque to front wheel, then the front wheel will roll and by rolling it causes forward motion of the chassis, then the back wheel will turn due to its center moves forward. so what's actually make the rear wheel to turn is because the force acting at the center right?
then based on this, http://cnx.org/content/m14385/latest/
the friction force will go backward. Where did i got wrong?

 

[jack action]

I think I can understand now. Thanks a lot!
If it is really a spool pulled by a rope, for r1 > 0.5r2, the spool will roll, while for r1 < 0.5r2, the spool will slide right?

I haven't checked the math for this particular problem (and I'm too tired to do it), but it is a possibility.

One last question will be, can you explain why for a front wheel drive, there is no friction acted on rear wheel? How to come to this conclusion?
I cannot understand this because the explanation i can think of is the engine will provide torque to front wheel, then the front wheel will roll and by rolling it causes forward motion of the chassis, then the back wheel will turn due to its center moves forward. so what's actually make the rear wheel to turn is because the force acting at the center right?
then based on this, http://cnx.org/content/m14385/latest/
the friction force will go backward. Where did i got wrong?

It's the rolling resistance - which is kind of related to the friction concept as it is the result of a constant times the normal force - that will turn the wheel. When the chassis pulls the center of the rear wheel, it tends to deform the tire (even if it was a steel wheel, it would still slightly deform) and the ground, which in turns causes rolling resistance and the wheel starts rotating.

In a simplified version, rolling resistance can be explained like this:

When the tire is deformed, the tire contact patch is shifted slightly forward and the vertical force reacting to the normal force is also shifted forward to stay in the center of the tire contact patch, which is not aligned with the center of the wheel anymore where the normal force is applied (the axle). This misalignment creates a couple which can be defined by the rolling resistance. If the normal force N is misaligned by an horizontal distance d, you can find the rolling resistance F_R of a tire with radius r like this:

Doing sum of moments:

F_R r = N d

or:

F_R = d/r N

where d/r is in fact the coefficient of rolling resistance.

 

[Poligon]

Hi Jack, thanks for your reply!
your reply made me understand somethings but at the same time some questions arose.
Below is a paragraph from here, http://cnx.org/content/m14385/latest/
[
When the external force is passing through center of mass, it only produces linear acceleration as there is no moment arm and, thus, there is no torque on the body. Linear acceleration means linear velocity tends to increase. This, in turn, induces tendency of the rolling body to slide in the forward direction (i.e. in the direction of force/acceleration). Force of friction, therefore, appears in the backward direction of external force to check the sliding tendency.
]
under the section 'The line of action of external force passes through center of mass'.
Based on the statement, it says force of friction (i think it refers to static friction) appears in backward direction to check the sliding tendency, which is somehow conflicting with your explanation and made me confused. I read through the website, and felt that it is logic; then i came across your explanation, which is also logical enough for me to believe in. Is it possible for you to point out which part of the web site's explanation that you think is inappropriate? so that i can clear my doubts.

Speaking of rolling resistance,
1. the term 'rolling resistance' is referring to a force or moment?
2. the force F_R (which is d/r N) is used to replace the effect of the resisting moment right? as in, when doing force analysis, we are not using the resisting moment (because it is hard to determine the exact value?), instead, we replace the resisting moment by a force (F_R), that can produce a similar effect as the resisting moment.
3. let say a wheel is rolling without slip from left to the right,
here's a statement from wiki,
[
The resulting pressure distribution is a-symmetrical and is shifted to the right. The line of action of the (aggregate) vertical force no longer passes through the centers of the cylinders. This means that a moment occurs that tends to retard the rolling motion.
]
so in this case, the aggregate vertical force actually caused a net counterclockwise torque, which actually resist the rotation. however, from hpwizard, i know that the direction of rolling friction is to the left, which is creating a torque that assist the rotation. why is this so? it seems conflicting to me.
I am so sorry for having so many questions to ask you. =(

 

[jack action]

Hi Jack, thanks for your reply!
your reply made me understand somethings but at the same time some questions arose.
Below is a paragraph from here, http://cnx.org/content/m14385/latest/
[
When the external force is passing through center of mass, it only produces linear acceleration as there is no moment arm and, thus, there is no torque on the body. Linear acceleration means linear velocity tends to increase. This, in turn, induces tendency of the rolling body to slide in the forward direction (i.e. in the direction of force/acceleration). Force of friction, therefore, appears in the backward direction of external force to check the sliding tendency.
]
under the section 'The line of action of external force passes through center of mass'.
Based on the statement, it says force of friction (i think it refers to static friction) appears in backward direction to check the sliding tendency, which is somehow conflicting with your explanation and made me confused. I read through the website, and felt that it is logic; then i came across your explanation, which is also logical enough for me to believe in. Is it possible for you to point out which part of the web site's explanation that you think is inappropriate? so that i can clear my doubts.

I don't think you should refer to this website to understand what affects a rolling tire because it is way too theoretical. Here's one paragraph from your link:

We have already learned in the previous module that no friction is involved in uniform rolling. We shall find in this module that friction is actually the agent, which enforces the condition for accelerated rolling. In doing so, friction causes linear and angular accelerations or decelerations, depending on the requirement of rolling motion.

That page is for accelerated rolling only. When you check the page about uniform rolling, you can read:

First, we shall revert to the definition of pure rolling. The motion of pure rolling is characterized by absence of sliding. Friction, on the other hand, comes in the picture only when there is sliding i.e. there is relative displacement of two surfaces. Here, there is only a point (not a surface) in contact with the surface, which is continuously being replaced by neighboring particles on the rim of the rolling body. Thus, there is no friction as there is no sliding of surfaces over one another.

(...)

Absence of friction for rolling at constant velocity has a very significant implication as a disk in uniform rolling shall move indefinitely, if no net external force/ torque is acting. This is a slightly unrealistic deduction for we know that all rolling disk is brought to rest ultimately unless external force is applied to maintain the speed. This needs explanation.

As a matter of fact, it is not possible to realize an ideal pure rolling in the first place. All rolling motion in our real world involves contact which spreads beyond a point and there is some amount of deformation involved and, therefore, existence of normal force constituting a torque in the opposite direction to rotation of the object. As such, the rolling body decelerates.

So all of this theory is about an ideal pure rolling, which doesn't exists in real life.

Speaking of rolling resistance,
1. the term 'rolling resistance' is referring to a force or moment?

A force.

2. the force F_R (which is d/r N) is used to replace the effect of the resisting moment right? as in, when doing force analysis, we are not using the resisting moment (because it is hard to determine the exact value?), instead, we replace the resisting moment by a force (F_R), that can produce a similar effect as the resisting moment.

Something like that.

3. let say a wheel is rolling without slip from left to the right,
here's a statement from wiki,
[
The resulting pressure distribution is a-symmetrical and is shifted to the right. The line of action of the (aggregate) vertical force no longer passes through the centers of the cylinders. This means that a moment occurs that tends to retard the rolling motion.
]
so in this case, the aggregate vertical force actually caused a net counterclockwise torque, which actually resist the rotation. however, from hpwizard, i know that the direction of rolling friction is to the left, which is creating a torque that assist the rotation. why is this so? it seems conflicting to me.

It depends if you look from the point of view of the tire or the one from the ground. For rolling resistance, the ground pushes on the tire such that it slows down the rotation. But the tire pushes on the ground - with an equal and opposite force - which causes the deceleration of the vehicle.

You would have the same «problem» with the friction force that accelerate the vehicle. If you're rolling from left to right and you want to accelerate, the friction force point to the right, even if it seems that it would go against the rotation of the tire. But from the point of view of the ground, the friction force is pointing in the other direction.

 

[Poligon]

Hi Jack, then i understand now. Thank you very much for your help!

 

[Poligon]

So can I summarized all the things as follow (the wheel rolls without slip):
for an accelerating torque (clockwise) acting on a wheel, causing it to roll from left to right,
the one that causes acceleration is static friction, which points to the right and other than that, there will be another force, the rolling resistance, which points to the left.

while for an decelerating torque (counter clockwise) acting on a wheel which is rolling from left to right,
the one that causes deceleration is static friction, which points to the left and other than that, there will be another force, the rolling resistance, which points to the left.For force acting off the center of a cylindrical body (like rope pulling a spool),
there will be 3 cases, either the body slips or it rolls without slip or it rolls with slip. for the case of rolls without slip, the forces acting at the wheel will be the same as the case of torque acting on the wheel, depending on whether the force causes clockwise or counter clockwise torque.The other condition will be:
for an accelerating force (to the right) that acts at the center of a wheel, causing it to roll from left to right,
there will be no static friction at the wheel, only rolling resistance, which increase the angular acceleration of the wheel and points to the left.

while for an decelerating force (to the left) that acts at the center of a wheel that rolls from left to right,
there will be no static friction at the wheel, only rolling resistance, which tend to increase the angular acceleration of the wheel and points to the left...
Hmm, everything does make sense until the final statement on decelerating force acting at the center of the wheel. Is this statement correct?
Also, to what extent of real life does the above summary goes?