I was doing this problem for self study in rotational dynamics:
Two discs are mounted on thin, lightweight rods oriented through their centers and normal to the discs. These axles are constrained to be vertical at all times, and the discs can pivot frictionlessly on the rods. The discs have identical thickness and are made of the same material, but have differing radii $p$ and $q$. The discs are given angular velocities of magnitudes $x$ and $y$, respectively, and brought into contact at their edges. After the discs interact via friction it is found that both discs come exactly to a halt. Which of the following must hold? Ignore effects associated with the vertical rods.
Answer choices:
- $(x^2)p = (y^2)q$
- $xp = yq$
- $x(p^2) = y(q^2)$
- $x(p^3) = y(q^3)$
- $x(p^4) = y(p^4)$
I got the answer $x(p^4) = y(p^4)$ by setting the angular momentum of the two discs equal to each other (because of conservation of momentum) and solving, but the answer is $x(p^3) = y(q^3)$. How do I solve this problem?
