xEXAMPLE

Two metal disks have masses m$1=3\mathrm{.}45$ kg and m$2=$UNKNOWN kg$,$ and each has a radius of $8\mathrm{.}31$ cm$.($You may ignore the inner hole for both disks $-$ assume that it is very small.$)$ They spin on cushions of air in a standard rotational dynamics apparatus. Initially, disk #$1$ is spinning counterclockwise at $6\mathrm{.}02$ rad$/$s and disk #$2$ is spinning clockwise at $2\mathrm{.}50$ rad$/$s$.$ A pin is removed that drops disk #$1$ onto disk #$2.$ After a short time they are seen to spin at the same angular speed of $2\mathrm{.}33$ rad$/$s$,$ counterclockwise. Assume that there are no outside frictional forces acting on the system of the two disks.

a$.$ Calculate the moment of inertia of the first disk. Include units.

$(0\mathrm{.}0119$ kg m$2)$

b$.$ Calculate the mass of the second disk in this ideal situation. Include units