An unskilled DJ is chewing some very dense (to be later thought of as a point mass) Big League Chew while spinning records with his pals. The platten and record combined appear as a "solid cylinder or disk" with a diameter of 30cm and a mass of 700 grams. The DJ is working in some kids theme music (let us suppose Disney), and the spindle speed is 45 RPM. All of a sudden the power goes out, the spindle experiences no external torques, and 350 grams of Big League Chew falls 6cm from the spindle. How fast is Disney going now?
Total rotational kinetic energy is conserved before and after the unfortunate incidence!
Rotational KE = (1/2)*I*w^2 = ...
In seven lines of explanations and computations, the problem is solved.