Why is rolling easier than sliding?

[haruspex]

There is conservation of angular momentum in the absence of any external torque. If you consider conservation of angular momentum for a wheel to be valid in "only a few idealised contexts", then you ought be be consistent and apply that to everything: no parabolic projectile motion (air resistance); no frictionless pulleys (friction); no massless strings or ropes (mass); etc. All of classical mechanics practically is an idealised context.

Newton's first law only applies in a few idealised contexts as well.

I wrote "in a few" idealised contexts. I should have omitted "idealised". You can take idealised versions of a ball rolling down a slope (no drag, no rolling resistance) and my point still stands. The only case that springs to mind where there is in principle no friction on a frictional surface is rolling on the level at constant speed.
I interceded because it appeared to be confusing the OP.

 

[PeroK]

I wrote "in a few" idealised contexts. I should have omitted "idealised". You can take idealised versions of a ball rolling down a slope (no drag, no rolling resistance) and my point still stands. The only case that springs to mind where there is in principle no friction on a frictional surface is rolling on the level at constant speed.
I interceded because it appeared to be confusing the OP.

The argument went along the following lines (to summarise):

Staring Premise: Rolling without slipping (even at constant speed on a level surface requires static friction)
Static friction is greater than kinetic friction, so rolling should be "harder" than sliding against kinetic friction

One rebuttal is that the static friction need not be the maximum possible; so perhaps only a small force of static friction is required to maintain rolling - whereas, kinetic friction is constant.

A second point is that, by conservation of angular and linear momentum, it takes no external torque or force to maintain constant rolling motion. The required force of static friction is zero in this case. I.e. even on a frictionless surface rolling without slipping may continue (theoretically at least).

To alter the state of motion (either accelerate or decelerate the wheel) while maintaining rolling requires an external force and external torque in the correct proportions. This can be achieved on a rough surface with static friction. This cannot be achieved on a frictionless surface.

 

[haruspex]

The argument went along the following lines (to summarise):
Staring Premise: Rolling without slipping (even at constant speed on a level surface requires static friction)

Up to the point in question, this was the exchange:

I learned that rolling involves the coefficient of static friction

Rolling doesn't involve any friction to continue.

Nothing there about "constant speed on a level surface". I'm sure that's what you had in mind when you made the remark, but I see no evidence it is what the OP had in mind. The OP appeared, unsurprisingly, somewhat confused.

 

[PeroK]

Up to the point in question, this was the exchange:Nothing there about "constant speed on a level surface". I'm sure that's what you had in mind when you made the remark, but I see no evidence it is what the OP had in mind. The OP appeared, unsurprisingly, somewhat confused.

We'll have to disagree about the reason for the OP's confusion. The textbook he quoted says that "rolling without slipping depends on static friction". That definitely gives me the impression that without friction an object simply cannot roll.

You could say "motion depends on an external force". That's true in general and, of course, in practice. But, you still have Newton's first law.

You do not need a force to have motion; and you do not need a torque to have rolling without slipping.

 

[haruspex]

The textbook he quoted says that "rolling without slipping depends on static friction".

Yes, that is a common error. Let's just say your response needed a little clarification.

 

[zoki85]

You could say "motion depends on an external force". That's true in general and, of course, in practice. But, you still have Newton's first law.

You do not need a force to have motion; and you do not need a torque to have rolling without slipping.

 

[anorlunda]

The OP has not been back on PF since post #32 last Monday, the thread is now up to #50.

The late Jim Hardy was fond of saying "A question well asked is half answered." I would like to challenge all of you to restate the OP question in a way that could have been answered without a big debate.

 

[jbriggs444]

OP has clarified his own confusion in #6 and #12:

In #6, he is speaking of his teacher's claim:

"If you lock your wheels driving down the road on dry concrete if they are sliding, or skidding, you will have less friction than if they are rolling. (µs > µk)
This is in theory the idea of antilock breaking systems (ABS)

In #12, he relates how the teacher's claim seems to run counter to his own experience:

If the explanation is correct, it's a fact that the static friction of rolling wheels is higher than the kinetic friction of sliding wheels, which is not experienced when I roll or slide a wheel on its own as it's much easier to roll the wheel probably because less friction is involved.

Rephrasing:

You can stop very much more quickly [by a factor of 20, perhaps] with the brakes locked up and the tires skidding than with the brakes not applied and the tires rolling freely as you gently coast to a stop.

You can stop even more quickly if the brakes are applied at a threshold such that the tires are rolling but are just on the verge of skidding.

Rolling involves static friction. Skidding involves kinetic friction. How can static friction result both in less retarding force than kinetic friction and in more retarding force than kinetic friction?

Edit: One wonders whether the PF denizens can spin this out for another +20 responses yet.

 

[kuruman]

The OP has not been back on PF since post #32 last Monday, the thread is now up to #50.

You mean #70.

The late Jim Hardy was fond of saying "A question well asked is half answered." I would like to challenge all of you to restate the OP question in a way that could have been answered without a big debate.

My interpretation of OP's original question is "Why is it easier (less energy required) to accelerate an object to a final speed $V$ when it is allowed to roll (e.g. bicycle with wheels free) than when it is not allowed to roll (e.g. bicycle with wheels rolled)". I responded accordingly with #3.

Rolling involves static friction. Skidding involves kinetic friction. How can static friction result both in less retarding force than kinetic friction and in more retarding force than kinetic friction?

Yes, OP seems to think that the effects of friction are of a similar nature. That was pointed out in #37. OP's confusion appears to stem from the following erroneous reasoning because of lack of understanding of the difference between static and kinetic friction (statement 3):
1. Static friction comes into play when objects are rolling on a surface.
2. Kinetic friction comes into play when objects are sliding on a surface.
3. The motion of an object is similarly affected by static and kinetic friction.
4. The coefficient of static friction is higher than the coefficient of kinetic friction.
5. Therefore it should be harder not easier to roll an object than to slide it, no?

 

[Saw]

I didn't read all posts and don't know what made this thread so long... Really leaving aside the semantic part (what should be called "static" versus "kinetic" and what deserves the name "friction" and what not), I would think that this explanation from Tipler should answer the OP:

"As the car moves down the
highway, the rubber flexes radially inward
where the tread initiates contact with the
pavement, and flexes radially outward where
the tread loses contact with the road. The tire
is not perfectly elastic, so the forces exerted on
the tread by the pavement that flex the tread
inward are greater than those exerted on the
tread by the pavement as the tread flexes back
as it leaves the pavement. This imbalance of
forces results in a force opposing the rolling of
the tire. This force is called a rolling frictional
force. The more the tire flexes, the greater the
rolling frictional force."

... though to be honest I myself have now doubts.

Does Tipler mean that when "the rubber flexes radially inward where the tread initiates contact with the pavement", that is like kinetic friction pushing the car back, but when it "flexes radially outward where the tread loses contact with the road" that is like static friction pushing it forward, so one thing would compensate for the other, as long as the collision were perfectly elastic without energy being lost due to deformation? If that were true the reply to the OP would be as easy as this: in rolling you have the same as sliding but compensated for, though not fully and that is why rolling is easier than sliding. But as I said, in the end I am not sure if this is the right interpretation of Tipler's text.

 

[Mister Perfessor]

The main stopping benefit of ABS brakes is to avoid the steep temperature rise at the skidding footprint, which softens the rubber and allows it to slough off, thus lubricating the interface, leaving the skid mark and lowering the available stopping force. On ice, the reverse occurs; the surface of the ice under the tire melts in a skid, also best avoided for the shortest stop. On gravel ABS makes little difference, except maintenance of control (important in all three situations).
At least that's how my aircraft maintenance instructor explained it all those years ago.

I agree with that, as the coefficient of friction between the tire's contact patch and the road surface is a variable, and that very aggressive braking will alter that state dramatically. Temperature rise inside the tire & the road surface play a very important role

Just consider the brake pads & rotor on that wheel in two different cases. In a static condition with the car at rest, the brakes applied to a preset hydraulic pressure, and with a long lever temporarily attached to the wheel - measure the amount of torque it takes to get the brake rotor to slip across the brake pads holding it in place. Then compare that torque to what is available in a kinetic case, where the car is moving before the brakes are applied. That adds a thermal effect to both the brake rotor and the pads. The pad material will exhibit very interesting behaviors, one of which is the generation of gases that act to lubricate the contact point between the pads and the rotor. So the standard rotor should have two versions, one a plain rotor and another as a vented type. My point though, is that you will always find a much higher braking force is possible when the car is at rest before applying the brakes

If for example, a tilt table were to be built, large enough to carry the car in question. And that this table were to be covered with the same exact material as used on a test track located at the same facility. And then install in the test car a simple pendulum with a damping mechanism to steady it's position. Park the car on top of the tilting table and while holding the brakes at a set pressure, tilt the table forwards until the car slips (safety straps would be used to limit the slip to a safe distance, say 4") Now take this car out on the test track and perform a stopping distance test. No matter how small you can get that stopping distance, the pendulum will never reach as high up it's scale as when the car was on the tilt table. This is in my opinion mostly due to the effects of thermal rise at various points, which can be viewed in a simple manner as the exchange of energy required to slow the car

But the OP wasn't asking for real-world conditions. I would only suggest adding the effects of temperature rise to the hypothetical 'rubber tire rolling down an incline' model

 

[A.T.]

...why is it easier to roll the wheel than to slide it?

Because the rolling resistance is usually smaller than kinetic friction.

To see that the above is only usually true, one might consider a counter example:

A very soft wheel on a hard surface can be easier to slide, than to roll.

This is because in rolling both the wheel and the surface are being continuously deformed. In sliding only the surface is continuously deformed, while the wheel adopts an approximately constant deformation. So if you make the kinetic friction and the surface deformation low, then sliding becomes more efficient.