# Does Rolling Necessitate Static Friction?

## Main Question or Discussion Point

If smooth rolling motion does not necessitate static friction, which I have been led to believe by a certain @haruspex , then what other forces or principles could prevent a smoothly rolling body from slipping?

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Orodruin
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What haruspex is telling you is that when a wheel is rolling with constant velocity, then there is no need for a frictional force to maintain the roll without slipping. If you lifted the wheel from the ground (while maintaining the horizontal velocity), the lower part of the wheel would still be at relative rest with respect to the ground. Of course, this is assuming that the wheel spins without resistance.

Sorry, I was just thinking that maybe I should link the thread. I'll make sure to do that in the future.

Okay, I think this is starting to make some sense to me. Thank you.

A.T.
when a wheel is rolling with constant velocity, then there is no need for a frictional force to maintain the roll without slipping.
Also, if you accelerate the wheel by applying an appropriate amount of both: linear force and torque, then there is also no need for a frictional force. Only if there is a mismatch of force and torque, there is static friction or sliding.

Chestermiller
Mentor
Also, if you accelerate the wheel by applying an appropriate amount of both: linear force and torque, then there is also no need for a frictional force. Only if there is a mismatch of force and torque, there is static friction or sliding.
I find this very confusing (and I think the OP will also). Can you please elaborate on this.

Chet

A.T.
Can you please elaborate on this.
Consider a wheel on perfect ice (zero friction), with a torque and force applied at the axle, such that:

$a = \alpha * r$

Is there any slippage at the contact point? Is there static friction if you replace the ice with a high traction surface?

Chestermiller
Mentor
Consider a wheel on perfect ice (zero friction), with a torque and force applied at the axle, such that:

$a = \alpha * r$

Is there any slippage at the contact point? Is there static friction if you replace the ice with a high traction surface?
So, in the case of ice, when you are referring to torque, you are not referring to the torque that the road exerts on the tire, correct?

A.T.
So, in the case of ice, when you are referring to torque, you are not referring to the torque that the road exerts on the tire, correct?
Correct, in both cases, by applied force/torque I mean those applied to accelerate the wheel, eventual static friction not included. If you balance those correctly, you can accelerate without slippage or static friction.

Chestermiller
Mentor
Correct, in both cases, by applied force/torque I mean those applied to accelerate the wheel, eventual static friction not included. If you balance those correctly, you can accelerate without slippage or static friction.
You can see where I was confused. I thought you were referring to the acceleration of the car.

Chet

Dale
Mentor
if you accelerate the wheel by applying an appropriate amount of both: linear force and torque, then there is also no need for a frictional force
Does this mean that you believe that an automobile accelerates without static friction under normal circumstances? (Eg level road, not being towed or pushed etc)

A.T.
Does this mean that you believe that an automobile accelerates without static friction under normal circumstances? (Eg level road, not being towed or pushed etc)
No, I wasn't talking about a car under normal circumstances, and neither does the OP or the other linked thread this came from.

A car under the circumstances you state would require friction at least one wheel during acceleration. And while it would be technically possible to achieve zero friction on the other wheels, it is certainly not the case for a normal car.

Merlin3189
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I wonder if it would help to think of a ball (rolling), or rather, rotating about an axis perpendicular to the plane parallel to its direction of motion and passing through its CoG and point of contact with the plane surface on which it is sliding/rolling/or whatever you call it , BUT with the sense of rotation such that the momentary top of the ball is stationary and the point of contact (of the ball) is moving at twice its the velocity of the ball. Provided there were no external forces acting on the ball (thinking esp. of friction type forces at the point of contact) then it should continue in its happy path spinning with joy as it goes.
It seems obvious that, not only is friction not required, it is required not to be there. And having gone to all that trouble defining my axis of rotation, I could have used any axis and any sense of rotation I liked, and it would make no difference provided there were no friction type forces. (If no gravity, then no forces at all, but if gravity, then a pure normal reaction acting through point of contact and CoG parallel to gravity.)

If smooth rolling motion does not necessitate static friction, ..., then what other forces or principles could prevent a smoothly rolling body from slipping?
As others have said (I think) and as I have illustrated (I hope) slipping or not in the direction of motion is simply not an issue. In the absence of friction any relative motion at the point of contact is irrelevant as it does not cause any force on the ball.
Maybe you thinking that the ball might slide sideways if there were no friction? But again if there are no forces, there is nothing to change either its translational velocity or its rotation.

But then I wonder if by "preventing ...rolling body from slipping" you are thinking of maintaining synchronicity between the rotational motion and the translational? Rolling suggests the special case of combined rotation and translation, where the axis is perpendicular to the translation and the point of contact is momentarily stationary. In a non-ideal situation, with friction dissipating energy, it is also friction which provides the force to maintain the balance between rotation and translation to preserve this special case.
In the ideal case of no friction on an infinite flat plane the question never arises, because the translation and rotation never change.
Perhaps you are asking, what, in the absence of friction, can maintain this special case if something else altered the velocity or the rotation? Say perhaps the ball is charged and you suddenly put a like charge behind to accelerate the translation. Then you destroy the special case of rolling by increasing the translational speed while leaving the rotation unchanged (unless I'm missing some subtle electromagnetic effect), so that the point of contact is now not stationary and the ball is sliding. Similarly, if you apply a sideways force to change the direction of translation, the rotation continues on the same axis as in a gyro with the point of contact sliding sideways.

Even if the ball accelerated or decelerated its angular rotation without any external forces (say its moment of inertia was changing due to symmetric internal movement of mass), then in the absence of friction, the synchronicity is broken and the ball slides.

I wonder whether your question stems from the ubiquity of rolling of round objects in a world of friction? Were there no friction, I think rolling (as I define it here) would be an extremely rare almost impossible form of movement, liable to be destroyed by the slightest external force.

I wonder if it would help to think of a ball (rolling), or rather, rotating about an axis perpendicular to the plane parallel to its direction of motion and passing through its CoG and point of contact with the plane surface on which it is sliding/rolling/or whatever you call it , BUT with the sense of rotation such that the momentary top of the ball is stationary and the point of contact (of the ball) is moving at twice its the velocity of the ball. Provided there were no external forces acting on the ball (thinking esp. of friction type forces at the point of contact) then it should continue in its happy path spinning with joy as it goes.
It seems obvious that, not only is friction not required, it is required not to be there. And having gone to all that trouble defining my axis of rotation, I could have used any axis and any sense of rotation I liked, and it would make no difference provided there were no friction type forces. (If no gravity, then no forces at all, but if gravity, then a pure normal reaction acting through point of contact and CoG parallel to gravity.)

As others have said (I think) and as I have illustrated (I hope) slipping or not in the direction of motion is simply not an issue. In the absence of friction any relative motion at the point of contact is irrelevant as it does not cause any force on the ball.
Maybe you thinking that the ball might slide sideways if there were no friction? But again if there are no forces, there is nothing to change either its translational velocity or its rotation.

But then I wonder if by "preventing ...rolling body from slipping" you are thinking of maintaining synchronicity between the rotational motion and the translational? Rolling suggests the special case of combined rotation and translation, where the axis is perpendicular to the translation and the point of contact is momentarily stationary. In a non-ideal situation, with friction dissipating energy, it is also friction which provides the force to maintain the balance between rotation and translation to preserve this special case.
In the ideal case of no friction on an infinite flat plane the question never arises, because the translation and rotation never change.
Perhaps you are asking, what, in the absence of friction, can maintain this special case if something else altered the velocity or the rotation? Say perhaps the ball is charged and you suddenly put a like charge behind to accelerate the translation. Then you destroy the special case of rolling by increasing the translational speed while leaving the rotation unchanged (unless I'm missing some subtle electromagnetic effect), so that the point of contact is now not stationary and the ball is sliding. Similarly, if you apply a sideways force to change the direction of translation, the rotation continues on the same axis as in a gyro with the point of contact sliding sideways.

Even if the ball accelerated or decelerated its angular rotation without any external forces (say its moment of inertia was changing due to symmetric internal movement of mass), then in the absence of friction, the synchronicity is broken and the ball slides.

I wonder whether your question stems from the ubiquity of rolling of round objects in a world of friction? Were there no friction, I think rolling (as I define it here) would be an extremely rare almost impossible form of movement, liable to be destroyed by the slightest external force.

I am inclined to think rolling, as you have defined it with synchronicity would be impossible without static friction. How would the synchronicity even begin without static friction to get it started?
Without friction, the ball would either spin in place or slide, or a combination of the two but it would not roll with synchronicity.

A.T.
How would the synchronicity even begin without static friction to get it started?
See post #6.

See post #6.
Then you are not talking about a wheel rolling on a surface at all. Rolling implies translational movement resulting from turning over on an axis while in contact with a surface. It is friction with that surface that applies the torque at the edge of the wheel to start the rolling and the synchronicity to prevent slipping.
What you are describing is a wheel that is turning on axis but the translational movement is due entirely to a lateral force applied on the axle. That is spinning while translating but does not meet the conditions of rolling. In fact, this type of movement does not even need to involve a surface at all. I would also like to know how the wheel even begins to turn with synchronicity in this case. Does it require special additional synchronizing equipment? Perhaps an optical scanner to scan the surface and measure translational velocity, a microprocessor to coordinate the torque and angular velocity at the axle as well as the lateral force to see that your very *special* conditions are met? If so, what has any of this simulated rolling have to do with the physics of a wheel that is rolling on a surface?

A.T.
That is spinning while translating but does not meet the conditions of rolling.
That's just a semantic issue of the definition of "rolling". The kinematics is the same as in rolling.

If so, what has any of this simulated rolling have to do with the physics of a wheel that is rolling on a surface?
This condition on applied force vs. torque is useful to determine the direction of static friction, because it defines the boundary between forward & backward static friction.

That's just a semantic issue of the definition of "rolling". The kinematics is the same as in rolling..
No, it is a definitional issue. Rolling must have a distinct meaning otherwise any body that is both spinning and translating can be said to be rolling. Would you say the earth rolls around the sun? You are confusing precise definitions with semantic issues. Besides that, the kinematics are not the same. Do you think rolling resistance is the same on a frictionless surface?
This condition on applied force vs. torque is useful to determine the direction of static friction, because it defines the boundary between forward & backward static friction.
It may be useful as a model for some purposes but I don’t see how it answers the question raised by the OP and in fact gives the false impression that rolling on a surface without friction is possible when it isn’t.

A.T.
the kinematics are not the same.
Kinematics is the movement. The kinematics condition on clean rolling is:

$v=\omega * r$

It may be useful as a model for some purposes
The direction of static friction during rolling is a common question here on PF and this is the general answer to it.

Kinematics is the movement. The kinematics condition on clean rolling is:

$v=\omega * r$.
I tend to think a thorough kinematic analysis of a rolling object should include rolling resistance as in this example.

Determination of Tenpin Bowling Lane’s Rolling Resistance Based on Kinetics and Kinematics Modeling

The direction of static friction during rolling is a common question here on PF and this is the general answer to it.
As I say, it may serve some purpose but it doesn't answer the question raised by the OP and if it leaves people with the impression that static friction is not required for smooth rolling on a surface, then it is misleading.

Merlin3189
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... The kinematics condition on clean rolling is:

$v=\omega * r$

The direction of static friction during rolling is a common question here on PF and this is the general answer to it.
Apologies for my ignorance, but I'm not familiar with the symbols/notation here. Could you just explain it a bit for me please?
I assume $\omega$ is the vector representing the rotation, $v$ is the vector representing the translation and $*$ is the cross product symbol.
What vector is $r$?

If I'm wrong about * being the cross product symbol and r is just the radius of the ball with * being simple multiplication, how do you know the direction of the rotation vector?
For the kinematics condition, does it matter what the direction of rotation is and whether the point of contact is stationary or not?

I'm interested in this because you say it is the general answer to all the questions on static friction during rolling on PF and I find some of these discussions very confusing.

A.T.
As I say, it may serve some purpose but it doesn't answer the question raised by the OP and if it leaves people with the impression that static friction is not required for smooth rolling on a surface, then it is misleading.
It does answer it. Static friction of the ground on a rolling wheel can be backwards, forwards or zero depending on the force and torque that are applied to it otherwise.

You seem to be saying, in effect, that it is possible for a wheel to roll on a frictionless surface as long as you have a special means to exert all the forces on that wheel that friction would otherwise exert. All that amounts to is simulating the friction itself!
To me, it sounds the same as saying it is possible to fly in an airplane without wings, as long as you have a way to exert all the aerodynamic forces the wings would otherwise exert. It is hard to disagree with such a statement, but it is a rather bizarre thing to say to someone who is trying to understand how an airplane works or how a wheel rolls.
I find it very confusing and misleading and little to do with understanding the physics involved in a rolling wheel, to say a wheel can roll smoothly on a surface without friction…..as long as…….

A.T.