Understanding Rolling Motion: Friction Forces and Velocity Changes

[xOrbitz]

Homework Statement

(i) Suppose there's an object rolling without slipping at any surface.
(ii) Now, let's say a disk is rolling and slipping toward the +x direction

2. The attempt at a solution
(i) If the surface is horizontal then it won't apply any friction force on the object regardless on the surface composition, right? Because if the normal force between the object and the table has the same magnitude, then the existence of a frictional force in the horizontal direction would exert a horizontal acceleration on the object, changing it's velocity and therefore the velocity in the point of contact between the object and the surface wouldn't be equal to zero, is that correct?
(ii) Does it means the friction will be also in the +x direction? If so, then the acceleration exerted by the frictional force would rise the translational speed toward the +x direction making the object slide toward this direction because now we have that v_bottom > 0, am I getting it right?

_{Ps: The index is to make it easier to answer the questions (:}

 

[haruspex]

You are right that a disc rolling at constant velocity on a horizontal surface, no drag or rolling resistance, would not experience a frictional force.
I didn't understand the reference to magnitude of the normal force. Also, it was not necessary to mention the velocity "in the point of contact". That only covers kinetic friction. There cannot be static friction either since that would change the velocity of the disc as a whole, even though the velocity at the point of contact remains zero.

In (ii), you don't specify which way it is slipping. It could be rotating too fast for its linear speed, in which case there will be kinetic friction acting on it in the forward direction (increasing linear speed while reducing rotational speed); or rotating too slowly for its forward motion, in which case the kinetic friction will act in the backward direction, increasing its rotation while slowing its linear advance.

 

[mfb]

The rolling disk would experience friction - rolling friction. Not in an ideal world, but with real objects certainly. You need an external force to keep it rolling at a constant velocity, otherwise both linear and rotational motion reduce at the same time.

See haruspex for (ii).

 

[haruspex]

The rolling disk would experience friction - rolling friction. Not in an ideal world, but with real objects certainly. You need an external force to keep it rolling at a constant velocity, otherwise both linear and rotational motion reduce at the same time.

See haruspex for (ii).

Hi mfb,

By "rolling friction", do you mean rolling resistance? If so, yes, in the real world there would be rolling resistance, but in consequence there would likely also be some horizontal static friction. The direction of that friction depends on the details of the rolling resistance.

If the resistance arises principally from deformation of the floor, the disc is effectively rolling uphill. The normal force has a horizontal component acting backwards. Rotational inertia will tend to make the disc rotate too fast for its reducing linear speed, leading to forward static friction.

If the resistance arises principally from imperfect elasticity of the disc, the normal force is stronger on the leading part of the contact area than on the trailing part. This leads to a torque opposing rotation. Friction now acts in the backward direction, assisting rotation and keeping it consistent with the linear motion.

 

[mfb]

Rolling friction = rolling resistance, yes.

 

[xOrbitz]

You are right that a disc rolling at constant velocity on a horizontal surface, no drag or rolling resistance, would not experience a frictional force.
I didn't understand the reference to magnitude of the normal force. Also, it was not necessary to mention the velocity "in the point of contact". That only covers kinetic friction. There cannot be static friction either since that would change the velocity of the disc as a whole, even though the velocity at the point of contact remains zero.

In (ii), you don't specify which way it is slipping. It could be rotating too fast for its linear speed, in which case there will be kinetic friction acting on it in the forward direction (increasing linear speed while reducing rotational speed); or rotating too slowly for its forward motion, in which case the kinetic friction will act in the backward direction, increasing its rotation while slowing its linear advance.

Well, I just quoted the normal force to clarify that there's no motion in the vertical direction, but anyways, your answer clarified some nebulous doubts I had, I'm going to look forward some exercises now to see if I understood it correctly, thanks for the support.