A better understanding of rolling friction

[takando12]

" At every instant ,there is just one point of contact between the body and the plane and this point has no relative motion, hence ideally the friction should be zero" --from my textbook
Firstly, I don't understand the "relative motion" part. Can someone please explain.
And we do know in fact that there is some friction that exists int he form of rolling friction. But what exactly causes it when there is hardly any surface area of contact? Why is there any rolling friction at all?

 

[Geofleur]

The velocity of the point of contact has zero instantaneous velocity relative to the plane. Proof. For definiteness, assume the body is a cylinder rolling with angular velocity $\omega$. Then a point on the rim of the cylinder has velocity $v = R \omega$, where $R$ is the radius of the cylinder. Imagine there is thread wound around the cylinder. After a time $\Delta t$, an amount of thread $\Delta s = R \omega \Delta t = v \Delta t$ is unwound. Therefore, the ground covered by the cylinder in a time $\Delta t$ is also $\Delta s / \Delta t = v$. The speed of a point on the rim of the wheel is the same as the linear speed of the wheel as a whole. Now consider the system from the point of view of a reference frame that is stationary wrt the center of the cylinder. When a point on the rim is in contact with the plane, the point and plane velocity vectors have the same directions and magnitudes. Hence, the velocity of the contact point relative to the ground is zero.

I can think of at least one source of rolling friction: The wheel deforms under gravity as it rolls, and some of the energy that would go into rolling goes instead into deformations of the wheel, which in turn are dissipated as heat.

 

[sophiecentaur]

from my textbook

Haha. This is the problem. They make out that friction is 'ideal' - as far as they want to and then they are surprised that people get confused.
I got to thinking about friction and I realized that, because static friction can be given a Coefficient that works over a large range of loads, it's assumed that rolling friction can be treated the same. It is clearly daft to say that there is 'point contact' between a wheel and the ground. Even with a steel wheel on a steel rail, there will be a curved dent in the plane and it is the distortion causing rubbing between the differentl radii of the internal and external curves (gives rubbing and a force times a speed = work), along with hysteresis (Geofleur's point ,above), that causes the energy loss. Without the rolling friction, and ideal static friction would allow a driving force to work unimpeded and losslessly. Or, if the wheel is not driven, the static friction would just rotate the free wheel with no loss of energy.
Coefficient of Friction is a bit like Coeficient of Restitution. They both cover a multitude of factors which disturb the 'thinking person'.
Here's a thought to show that the whole thing is over simplified. If friction in the wheel bearings can be ignored and the thing is happening in a vaccuum, how would there be any rolling resistance at all, if the only contact force were horizontal? Does the elem,entary model take care of that?

 

[rcgldr]

It's not clear if the book is ignoring rolling resistance

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

or the possibility of a friction force between tire and pavement, such as the force that the ground exerts on a tire to oppose internal friction, and/or the opposing force of aerodynamic drag, and/or rolling resistance, and/or acceleration. The friction force between tire and pavement is a pair of Newton third law forces, the force that the tire exerts onto the pavement, and the force the pavement exerts onto the tire.

 

[takando12]

So there is some rolling friction because of temporary deformation of the surface and so more than just a point is actually in contact with the floor or plane.
While we're still on topic, what about the friction related to a cars tires?
Friction is responsible for the acceleration of the car. Is this rolling friction we're talking about?

 

[Geofleur]

Rolling friction impedes rolling. It's static friction that keeps the wheel from slipping on the road.

 

[takando12]

Rolling friction impedes rolling. It's static friction that keeps the wheel from slipping on the road.

I am sorry, but I can't understand. Please bear with me.
What exactly does slipping mean? aren't the wheels moving? How can it be static friction?

 

[sophiecentaur]

It may help if we re-run all this without mentioning the F word. The problem is in the name.
Imagine a rack and pinion railway locomotive. The wheel turns and the pinion pushes (backwards) against the rack. The (X_forward) reaction force causes the train to accelerate forwards. In between the rack and the pinion teeth there is a heavy sticky, tarry substance which absorbs energy every time it is squished and relaxed. It is a constant drain on the power delivered to the pinion. This is the equivalent of a force (X_backwards) on the train - to account for the loss of power (Work is force times speed). What's left, to accelerate the train is X_net, which is X_forward - X_backwards. Transfer the argument to a motor car with squishy rubber tyres etc.. The way we normally describe the two forces is Static Friction and Rolling Friction. When accelerating, they happen to act in opposite directions - so what?. When you are braking, they act in the same direction and they both slow the car down. The rolling friction when driving though wet sand will be the main contribution to limiting the car's speed. When driving at 70mph on a smooth road, the main contribution will be air drag and there will be bearing losses and a few more. People tend to lump them all together and include them in Rolling Resistance.
Classifying a force as "Friction" serves to confuse pretty well everyone who comes across it, in this case. Friction can act in two directions at once. OOO MMM GGG !

 

[CWatters]

" At every instant ,there is just one point of contact between the body and the plane and this point has no relative motion, hence ideally the friction should be zero" --from my textbook
Firstly, I don't understand the "relative motion" part. Can someone please explain.

They are deliberately ignoring rolling resistance.

Have a think about the motion of a wheel on a car. Think about the top and bottom of the wheel. If the car is moving at 20mph then (relative to the road) the top of the wheel is moving at 40mph and the bottom of the wheel at 0mph. There is no relative motion between the bottom of the wheel and the road. You only have actual relative motion between the bottom of the wheel and road when you skid or accelerate so hard that the wheels slip.

If the car is ideal (no drag, no friction, no rolling resistance) then it doesn't need an engine or friction to continue rolling along at a steady speed.

If the car is not ideal then an engine and friction is required to overcome forces such as air resistance or rolling resistance. In this situation the friction you need for the car to move is static friction because there is no actual relative motion between the bottom of the wheel and the road. However the bottom of the wheel is trying to move relative to the road.

If you brake so hard you lock the wheels and start skidding then there is relative motion at the bottom of the wheel. In this case what slows you down is kinetic friction.

And we do know in fact that there is some friction that exists int he form of rolling friction. But what exactly causes it when there is hardly any surface area of contact? Why is there any rolling friction at all?

As a rubber wheel rotates the tyre is squashed and then released as it goes past the contact point with the ground. The rubber of a tyre is not an ideal spring. It takes energy to squash the tyre and you don't get it all back when the tyre expands. Some is lost as heat. More in here..

https://en.wikipedia.org/wiki/Rolling_resistance

 

[sophiecentaur]

this point has no relative motion,

When you walk, your foot is in contact with the ground and there is no relative motion until you lift it and bring it forward for the next step. A wheel is like an endless supply of feet that each spend an instant in contact with the ground with no relative motion and then they go round, over the top of the wheel and meet the ground once again.

 

[Doc Al]

" At every instant ,there is just one point of contact between the body and the plane and this point has no relative motion, hence ideally the friction should be zero" --from my textbook

If you forget about rolling resistance for the moment, that quote requires a bit of context. Just because there's no relative motion of the point of contact does not imply that friction should be zero. What situation was the textbook describing?

 

[takando12]

Sorry for the late reply.
I think I've got the "relative velocity" part thanks to Cwatters and sophiecentaur.
So what prevents the wheel form actually moving or "slipping" is static friction or it tends to prevent any actual moving or skidding. Static friction acts in the forward direction and this accelerates the car.Coming to rolling resistance. (that's where it's hazy), how is it acting backward? I just can't visualize it. Shouldn't it also be in the forward direction as it opposes rolling?
I suppose if I can understand this , the brakes will also be clear to me. Please help.

If you forget about rolling resistance for the moment, that quote requires a bit of context. Just because there's no relative motion of the point of contact does not imply that friction should be zero. What situation was the textbook describing?

My book does speak about rolling friction in later pages but the deformation explanation was not given.

 

[sophiecentaur]

Shouldn't it also be in the forward direction as it opposes rolling?

Think about it, what direction will be against the motion of the car? The wheels will actually have to push forward harder than if there was no rolling friction. It would not be so much of a problem is the word Rolling Resistance were used. You would be having less of a problem, I think. Just treat it as another force on the actual vehicle that requires work to be done.
I'm not surprised that the book doesn't go into the rolling friction in detail - it is counter intuitive and the authors may even not have thought too much about it.

 

[Doc Al]

Static friction acts in the forward direction and this accelerates the car.Coming to rolling resistance. (that's where it's hazy), how is it acting backward? I just can't visualize it. Shouldn't it also be in the forward direction as it opposes rolling?

Static friction opposes slipping between surfaces; rolling resistance opposes rolling. Without static friction, the wheel would slip backwards against the surface; thus friction will act in the forward direction to prevent that slipping.

Rolling resistance is a different animal and is caused by deformation. Since the wheels are rolling forward, rolling resistance will act backward. (As sophiecentaur suggests, think of it as just another force that must be dealt with.)

 

[takando12]

Okay. I've got a better understanding now.
Coming to breaks. So now as Cwatters explained, the wheels are locked and they begin to skid.There is relative motion between the wheels and the road.The friction which is now responsible for stopping the car completely is...? sophiecentaur said it's both static and rolling acting in the backward direction. And Cwatters said kinetic friction is responsible. Do both mean the same?
What about when a car is going at a constant velocity?
Static friction accelerates( or is it the diff between static and rolling?) the car. So does this situation mean the static and rolling friction are equal and cancel out?

 

[Doc Al]

Coming to breaks. So now as Cwatters explained, the wheels are locked and they begin to skid.There is relative motion between the wheels and the road.The friction which is now responsible for stopping the car completely is...? sophiecentaur said it's both static and rolling acting in the backward direction. And Cwatters said kinetic friction is responsible. Do both mean the same?

No, not the same. CWatters was talking about when the wheels are locked and skidding occurs. sophiecentaur was talking about normal braking where you avoid skidding.

What about when a car is going at a constant velocity? Static friction accelerates( or is it the diff between static and rolling?) the car. So does this situation mean the static and rolling friction are equal and cancel out?

If the car is moving at constant velocity, then the net force must be zero. Since there are resistive forces working against the car (air drag, rolling resistance) you need to maintain some forward static friction to keep moving.

 

[jbriggs444]

If the car is moving at constant velocity, then the net force must be zero. Since there are resistive forces working against the car (air drag, rolling resistance) you need to maintain some forward static friction to keep moving.

I would be hesitant to categorize "rolling resistance" as something that needs to be countered with a forward force from static friction. Rolling resistance is better modeled as a torque or couple (the increased upward force on the leading edge of the tire taken together with the decreased upward force on the trailing edge) which does not directly result in any net rearward force.

One can counter rolling resistance with torque from the engine (if cruising under power) or with rearward static friction from the ground (if coasting to a stop).

 

[Dale]

I would be hesitant to categorize "rolling resistance" as something that needs to be countered with a forward force from static friction. Rolling resistance is better modeled as a torque or couple (the increased upward force on the leading edge of the tire taken together with the decreased upward force on the trailing edge) which does not directly result in any net rearward force.

I think that it is hard, in principle, to separate out forces of the same type (contact forces) in the same direction (horizontal). But to support your approach of treating it as a torque, it should be noted that when a tire deforms not only is there increased pressure at the leading edge of the contact patch and decreased pressure at the trailing edge, but the center of contact patch is also shifted forwards which gives the normal force a small lever arm and therefore a torque.

 

[Doc Al]

I think that it is hard, in principle, to separate out forces of the same type (contact forces) in the same direction (horizontal). But to support your approach of treating it as a torque, it should be noted that when a tire deforms not only is there increased pressure at the leading edge of the contact patch and decreased pressure at the trailing edge, but the center of contact patch is also shifted forwards which gives the normal force a small lever arm and therefore a torque.

I thought that, in addition to being offset thus creating a torque, the resultant contact force had a horizontal component opposing the direction of rolling.

 

[Dale]

I thought that, in addition to being offset thus creating a torque, the resultant contact force had a horizontal component opposing the direction of rolling.

Yes, but as I mentioned it is kind of difficult to separate it out. I mean, how can you distinguish between a forward static friction of 2 N plus a backwards rolling resistance of 1 N vs a forward static friction of 1.9 N plus a backwards rolling resistance of 0.9 N?

 

[Doc Al]

Yes, but as I mentioned it is kind of difficult to separate it out. I mean, how can you distinguish between a forward static friction of 2 N plus a backwards rolling resistance of 1 N vs a forward static friction of 1.9 N plus a backwards rolling resistance of 0.9 N?

Good point.

 

[takando12]

Ok. Now there was this question asked. why does the proper inflation of tyres help save fuel?
So here's my reasoning. When the tyres are properly inflated, the contact area between the road and the tyre will be minimised,hence rolling friction will also be greatly minimised and we would travel a larger distance for a given amount of fuel.
Is this right?

 

[CWatters]

Under inflation increases the amount that the tyre is deformed and its that which increases rolling resistance. The effect on the contact area is secondary.

 

[takando12]

Got it. Thank you all for your patience. Today is my physics term exam. Fingers crossed.