Friction in rolling without slipping

In summary, for an object to roll without slipping on a surface, there must be friction present at the point of contact. However, there are scenarios where rolling without slipping can occur on a frictionless surface, as demonstrated by the example of a ball rolling on ice. This apparent contradiction can be resolved by understanding that the point of contact can still be instantaneously at rest on a frictionless surface, and the relationship between linear and angular velocity remains the same.
  • #1
pixel
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Consider an object, say a ball, rolling at a constant speed without slipping to the right on a horizontal surface. Let's consider the ideal case, so no deformation of ball or surface. For rolling without slipping to occur, there has to be friction (static friction as the point on the ball that is in contact with the surface is instantaneously at rest). But that leads to some apparent contradictions.

First, a net horizontal force (friction) on the ball would cause the speed of its c.m. to change, but the friction force does no work so it couldn't change the speed. Second, there is a net torque about the c.m. of the ball which would cause the rotational speed to change. Both contradict the assumption of rolling without slipping at a constant speed. How to resolve?
 
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  • #2
pixel said:
Consider an object, say a ball, rolling at a constant speed without slipping to the right on a horizontal surface. Let's consider the ideal case, so no deformation of ball or surface. For rolling without slipping to occur, there has to be friction (static friction as the point on the ball that is in contact with the surface is instantaneously at rest). But that leads to some apparent contradictions.

First, a net horizontal force (friction) on the ball would cause the speed of its c.m. to change, but the friction force does no work so it couldn't change the speed. Second, there is a net torque about the c.m. of the ball which would cause the rotational speed to change. Both contradict the assumption of rolling without slipping at a constant speed. How to resolve?
The net force acting on a wheel moving at constant velocity is zero. The magnitude of the static friction force is a reaction to the acceleration of the wheel. If the wheel it is not accelerating, the magnitude of the static friction force is zero.
 
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  • #3
pixel said:
For rolling without slipping to occur, there has to be friction
No there doesn't.
pixel said:
How to resolve?
Your assumption that there is a frictional force is incorrect.
 
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  • #4
pixel said:
But that leads to some apparent contradictions.
Just because you don't understand something does not mean it is a contradiction.

Rolling without slippling means that the point that has contact with the surface has instantaneous velocity = 0.

If a ball is rolling on a surface where there is friction, the point of contact will not slide against the surface and there will be no external torque from the force of friction.

Place an already spinning ball or cylinder on a surface where there is some friction. What would you observe regarding the angular velocity and the linear velocity of that object?
 
  • #5
malawi_glenn said:
Just because you don't understand something does not mean it is a contradiction.
I believe @Orodruin made this point to me in the not too distant past. I believe you and @kuruman were participating in that thread, as well. Speaking from experience, I know the feeling of encountering a knowledge gap...regularly!
 
  • #6
malawi_glenn said:
Just because you don't understand something does not mean it is a contradiction.

Rolling without slippling means that the point that has contact with the surface has instantaneous velocity = 0.

If a ball is rolling on a surface where there is friction, the point of contact will not slide against the surface and there will be no external torque from the force of friction.

Place an already spinning ball or cylinder on a surface where there is some friction. What would you observe regarding the angular velocity and the linear velocity of that object?
You maybe don't understand what an "apparent contradiction" is.

I said in my post that the contact point was at rest.

There can be rolling with slipping on a surface with friction, given the right conditions.
 
  • #7
pixel said:
You maybe don't understand what an "apparent contradiction" is.
An "apparent contradiction" is based upon your understanding of the situation.
pixel said:
For rolling without slipping to occur, there has to be friction (static friction as the point on the ball that is in contact with the surface is instantaneously at rest).
This is simply false. Do you understand this?
 
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  • #8
hutchphd said:
This is simply false.
One can demonstrate this as follows.
Consider the following setup:
1659930175836.png

black: asphalt (friction high enough to allow rolling without slipping at all points), grey: ice (no friction)
Release the ball, it will roll without slipping on the asphalt. On the ice, the point of contact will still be instantenously at rest, and the relation between v and ω will be v = ωR, just as before.
So clearly, the ball can roll without slipping even on a frictionless surface.
 
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Related to Friction in rolling without slipping

1. What is rolling without slipping?

Rolling without slipping is a type of motion where an object rolls along a surface without any slipping or sliding. This means that the point of contact between the object and the surface has zero velocity, resulting in no kinetic friction.

2. How is friction involved in rolling without slipping?

In rolling without slipping, there is still friction present between the object and the surface. However, this friction is static rather than kinetic. It acts to prevent slipping and allows the object to roll smoothly.

3. What factors affect the amount of friction in rolling without slipping?

The amount of friction in rolling without slipping is affected by the weight of the object, the surface it is rolling on, and the shape and material of the object. A heavier object or a rougher surface will result in more friction, while a smoother object or surface will have less friction.

4. Can rolling without slipping occur on any surface?

No, rolling without slipping can only occur on surfaces that are rigid and have a high coefficient of static friction. This means that the surface must be able to provide enough resistance to prevent slipping and allow for rolling without any sliding.

5. What are some real-life examples of rolling without slipping?

Some examples of rolling without slipping include a ball rolling down a ramp, a car driving on a road, and a wheel rolling on a flat surface. In all of these cases, the object is able to roll smoothly without any slipping or sliding due to the presence of friction.

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