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AlephNumbers
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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?
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.Orodruin said:when a wheel is rolling with constant velocity, then there is no need for a frictional force to maintain the roll without slipping.
I find this very confusing (and I think the OP will also). Can you please elaborate on this.A.T. said: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.
Consider a wheel on perfect ice (zero friction), with a torque and force applied at the axle, such that:Chestermiller said:Can you please elaborate on this.
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. said: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?
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 said: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?
You can see where I was confused. I thought you were referring to the acceleration of the car.A.T. said: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.
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. said: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
No, I wasn't talking about a car under normal circumstances, and neither does the OP or the other linked thread this came from.DaleSpam said: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)
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.AlephNumbers said:If smooth rolling motion does not necessitate static friction, ..., then what other forces or principles could prevent a smoothly rolling body from slipping?
Merlin3189 said: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.
So then the simple answer to your question is, nothing.
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.
See post #6.Tom_K said:How would the synchronicity even begin without static friction to get it started?
A.T. said:See post #6.
That's just a semantic issue of the definition of "rolling". The kinematics is the same as in rolling.Tom_K said:That is spinning while translating but does not meet the conditions of rolling.
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.Tom_K said: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. said:That's just a semantic issue of the definition of "rolling". The kinematics is the same as in rolling..
A.T. said: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.
Kinematics is the movement. The kinematics condition on clean rolling is:Tom_K said:the kinematics are not the same.
The direction of static friction during rolling is a common question here on PF and this is the general answer to it.Tom_K said:It may be useful as a model for some purposes
A.T. said:Kinematics is the movement. The kinematics condition on clean rolling is:
##v=\omega * r##.
A.T. said: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?A.T. said:... 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.
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.Tom_K said: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.
Physics is about quantifying things. To quantify the direction and magnitude of static friction during rolling you have to determine how far off the other forces are from the special case with zero static friction. So this special case is key to understand the physics of static friction during rolling in a quantitative manner.Tom_K said:I find it very confusing and misleading and little to do with understanding the physics involved in a rolling wheel...
Rolling necessitates static friction when an object is in motion on a surface with low friction, causing the object to rotate instead of sliding. This is due to the contact points between the object and the surface, which resist the motion and cause a force called static friction.
Rolling and sliding are both forms of kinetic friction, but they differ in how they occur. Rolling friction involves the rotation of an object, while sliding friction involves the sliding motion of an object. Rolling friction is usually lower than sliding friction due to the reduced surface area in contact with the surface.
No, rolling cannot occur without static friction. This is because the contact points between the object and the surface must provide a force to resist the rotation and allow the object to move forward. Without static friction, the object would simply slide instead of rolling.
The coefficient of static friction is a measure of the force required to initiate motion between two surfaces. In the case of rolling, the coefficient of static friction determines how much force is needed to overcome static friction and start the rolling motion. A lower coefficient of static friction will result in easier rolling.
The amount of static friction in rolling can be affected by various factors, including the nature of the surface, the weight and shape of the object, and the speed of the rolling motion. For example, a rougher surface or a heavier object will typically result in higher static friction and make rolling more difficult.