# 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.
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