# Spinning disk

**Classical Mechanics**Level 3

I spin up a solid disk of mass \(M\) and radius \(R\) to some initial angular velocity \(\omega_i\). I then place the disk on a table that has friction. The disk rolls and slips on the table until it reaches some angular velocity \(\omega_f\), at which point it rolls without slipping. What is the ratio \(\omega_f/\omega_i\)?

**Details and assumptions**

- The disk initially has no linear momentum.