# Friction on pure rolling non deforming sphere?

• B
• tbn032
In summary: No, the sphere will have one point of contact which will continuously change as the sphere rolls. The sphere will not slow down since there is no rolling resistance.

#### tbn032

How will the friction work on a sphere which is purely rolling on a horizontal surface such that both the sphere and surface does not deform. The sphere at any time t will only have one point of contact, which would continuously changing as the sphere rolls. Will The friction be applied to the sphere and will it stop rolling?. Since there is one point of which pass vertically through the center of mass, there would not be any counter torque due to normal forces. The velocity of contact point would be zero since it is pure rolling.

If the sphere and surface are not deforming, there is no rolling resistance, right? So you are only left with some air resistance opposing the sphere's linear movement, which will eventually slow the sphere to a stop.

tbn032 said:
The velocity of contact point would be zero since it is pure rolling.
True, but for a finite contact force, the pressure at the point of contact would be infinite, and so beyond the strength of any real material. Friction is independent of the area of contact or pressure. Friction is proportional only to the total contact force.

It is the locus of the contact point that moves as the object rolls, not the contact point. In your ideal geometric model, each contact point exists for only one instant. Without time, the contact point cannot have a velocity, but the locus of all the instant contact points does have a velocity.

tbn032 said:
How will the friction work on a sphere which is purely rolling on a horizontal surface such that both the sphere and surface does not deform. The sphere at any time t will only have one point of contact, which would continuously changing as the sphere rolls. Will The friction be applied to the sphere and will it stop rolling?. Since there is one point of which pass vertically through the center of mass, there would not be any counter torque due to normal forces. The velocity of contact point would be zero since it is pure rolling.
You mean "how does friction work between a frictionless object and a frictionless surface?"

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