Rolling of non-deforming sphere on a non-deforming rough surface?

In summary, rolling friction is the static friction applied by a rough surface on a moving object, increasing angular acceleration and decreasing translational velocity until v=Rw is reached. Rolling resistance is the counter torque caused by deformation of the object or surface. In a hypothetical scenario with no external forces, friction may still occur and stop a sliding object. However, in real scenarios, friction is a reaction to other forces and cannot exist without them.
  • #1
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According to my current understanding
rolling friction
rolling friction is the static friction (parallel to the surface on which the object is moving) applied by the frictional surface (rough surface) on the contact point or contact area of the object whose v≠Rw(v is translational velocity and R is radius of sphere and w in angular velocity).It increases the angular acceleration and decreases the translational velocity or vice versa till the condition v=Rw is reached.

Rolling resistance
Rolling resistance is the counter torque provided to the rolling object due to the deformation of the object or the surface, causing the normal forces to shift from the centre of mass and thus providing counter torque.

Now my question is.
Suppose a non deforming sphere of radius R initially is kept on a non deforming rough horizontal surface(frictional surface). Then it is provided with translation velocity v and angular velocity w such that v=Rw.will the static frictional force(rolling friction) be applied on the sphere?will the sphere continue to roll forever?(there is no air resistance and there is no rolling resistance due to non deforming sphere and non deforming horizontal surface)(gravitational forces acts on the sphere perpendicular to the horizontal surface)
 
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  • #2
tbn032 said:
Now my question is.
Suppose a non deforming sphere of radius R initially is kept on a non deforming rough horizontal surface(frictional surface). Then it is provided with translation velocity v and angular velocity w such that v=Rw.will the static frictional force(rolling friction) be applied on the sphere?will the sphere continue to roll forever?(there is no air resistance and there is no rolling resistance due to non deforming sphere and non deforming horizontal surface)(gravitational forces acts on the sphere perpendicular to the horizontal surface)
Just like it happens between two flat surfaces, friction force only appears as a reaction to another force.
If nothing is pushing or pulling your sphere in the rolling direction, there is no acceleration or related forces.
 
  • #3
Lnewqban said:
Just like it happens between two flat surfaces, friction force only appears as a reaction to another force.
I think friction could appear in the absence of a force. Suppose a cube is sliding on a frictional horizontal surface with momentum p(no external force is being applied on the cube). Friction would still be applied on the cube(opposing the motion of the cube), and thus the cube will stop sliding.
 
  • #4
tbn032 said:
According to my current understanding
rolling friction
rolling friction is the static friction (parallel to the surface on which the object is moving) applied by the frictional surface (rough surface) on the contact point or contact area of the object whose v≠Rw(v is translational velocity and R is radius of sphere and w in angular velocity).It increases the angular acceleration and decreases the translational velocity or vice versa till the condition v=Rw is reached.

Rolling resistance
Rolling resistance is the counter torque provided to the rolling object due to the deformation of the object or the surface, causing the normal forces to shift from the centre of mass and thus providing counter torque.

Now my question is.
Suppose a non deforming sphere of radius R initially is kept on a non deforming rough horizontal surface(frictional surface). Then it is provided with translation velocity v and angular velocity w such that v=Rw.will the static frictional force(rolling friction) be applied on the sphere?will the sphere continue to roll forever?(there is no air resistance and there is no rolling resistance due to non deforming sphere and non deforming horizontal surface)(gravitational forces acts on the sphere perpendicular to the horizontal surface)
I thought you asked this question already. Friction applies in real scenarios. If you invent a hypothetical scenario, then there's no way to test whether there is friction or not.

Whether there is friction is part of the hypothetical assumptions.
 
  • #5
tbn032 said:
I think friction could appear in the absence of a force. Suppose a cube is sliding on a frictional horizontal surface with momentum p(no external force is being applied on the cube). Friction would still be applied on the cube(opposing the motion of the cube), and thus the cube will stop sliding.
I was referring to static friction at each instant the contact point of the sphere is in static contact with the perfecly flat surface.
But I believe that my previous statement is also valid for the case of the sliding cube, as Newton’s laws still apply: a change in momentum during certain time always generates a force that resists that change, and forces always come in pairs.
 

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