Friction in rolling without slipping

[pixel]

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?

 

[erobz]

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.

 

[Orodruin]

For rolling without slipping to occur, there has to be friction

No there doesn't.

How to resolve?

Your assumption that there is a frictional force is incorrect.

 

[malawi_glenn]

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?

 

[erobz]

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!

 

[pixel]

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.

 

[hutchphd]

You maybe don't understand what an "apparent contradiction" is.

An "apparent contradiction" is based upon your understanding of the situation.

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?

 

[malawi_glenn]

This is simply false.

One can demonstrate this as follows.
Consider the following setup:

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.