Required force for sphere start rolling

[eyeweyew]

Homework Statement

What is the required applied force to the center of mass of the sphere for it to start rolling on a surface?

Relevant Equations

μ[SUB]s[/SUB]⋅m⋅g

Assume there are two objects on the same surface, one is a cube and the other is a sphere. Both objects have the same mass m. The required applied force to the center of mass of the cube for it to start sliding should be equal to static friction force: μ_s⋅m⋅g.

But what is the required applied force to the center of mass of the sphere for it to start rolling? I assume it should be less than static friction force: μ_s⋅m⋅g?

 

[Orodruin]

This depends on rolling resistance, not friction (apart from that friction needs to be large enough for the ball to roll rather than slide).

 

[haruspex]

But what is the required applied force to the center of mass of the sphere for it to start rolling? I assume it should be less than static friction force: μ_s⋅m⋅g?

Consider torques about the point of contact with the surface. What torques are there?