Rotating with slipping to rotating without slipping?

[nomnom123]

Homework Statement

This is a problem that I encountered in my physics project. I'm attempting to model an object (a hula hoop) that begins by rotating with slipping, but transitions into rotating without slipping at a certain point. How/when does this transition happen?

Relevant Equations

torque = inertia x angular acceleration

It seems to me that this transition implies going from kinetic friction to static friction. The kinetic friction would apply a torque that would slow down the object's angular velocity, but I'm not sure how this connects to the object suddenly transitioning into rotating without slipping.

 

[PeroK]

Problem Statement: This is a problem that I encountered in my physics project. I'm attempting to model an object (a hula hoop) that begins by rotating with slipping, but transitions into rotating without slipping at a certain point. How/when does this transition happen?
Relevant Equations: torque = inertia x angular acceleration

It seems to me that this transition implies going from kinetic friction to static friction. The kinetic friction would apply a torque that would slow down the object's angular velocity, but I'm not sure how this connects to the object suddenly transitioning into rotating without slipping.

It doesn't suddenly transition. Gradually the rotation increases and the linear speed decreases until there is a balance that equates to rolling without slipping.

 

[TSny]

It seems to me that this transition implies going from kinetic friction to static friction.

This is not quite correct if you are assuming that the rolling takes place on a horizontal surface. Is static friction required for rolling without slipping?

 

[CWatters]

While rotating with slip there is a force on the hoop that will both accelerate the hoop (change its linear velocity) and slow it's rate of rotation. At some point the linear velocity and rotational velocity will be consistent with rotation without slip.

As soon as that point is reached the friction force reduces to zero. The hoop rolls along at a constant speed without any tendency to slip.

The above assumes it's rolling on a flat surface and things like air and rolling resistance can be ignored.