Maximum force pulling a wheel without it slipping

[WinterGrascph]

Homework Statement

We have a wheel with [mass = 1.5 kg] and a [radius = 0.06 m]. The static friction thing between the ground and the wheel is 0.3 . WIth how much force can we pull the string spooled around the wheel without the wheel slipping. The string ends at the top of the wheel and we pull it parallel to the ground.

Homework Equations

Torque, M = radius x force.
Maximum static friction, mass * g * 0.3.

The Attempt at a Solution

The maximum static friction between the ground and the wheel is 4.5 Newtons. I do not know how to factor in torque.

 

[azizlwl]

Maybe you specify the relationship between rotational and translational motion.

 

[andrewkirk]

As azizlwl says it depends on that relationship. To use the relationship you need the moment of inertia of the wheel. Did they give you that in the problem? If not, you can work it out if they give you the characteristics of the wheel. The simplest assumption is that it's a uniform disk, for which the moment of inertia can be found on this page under 'solid cylinder'.