Rolling disk, energy before pure rotational?

[kanki]

Suppose a solid disk of radius R is given an angular speed about an axis through its center and then lowered to a horizontal surface and released, the coefficient of friction between disk and surface is u. What is the distance traveled before pure rolling occurs?



Conservation of Momentum is applied because no net torque.



The work done by the friction of the disk, fx is used to find the distance x travelled. however i do not know which energy has been changed into work done by friction. What is meant by pure rolling? Only translational and rotational? I'm stuck here.

 

[Mentz114]

The initial energy of the disc is rotational and is given by -

$$E = \frac{1}{2}I\omega ^2$$

Pure rolling starts when the slipping stops, that is, when the torque due to friction is less than a certain value.