Answer
$M = 45.2 \ kg$
Work Step by Step
a) We know that angular momentum is conserved. Thus, we find the initial angular momentum. (Recall, we must convert rpm to radians per second.)
$L_i = I\omega=(.22)(13.61)=3$
Using the equation for the moment of inertia of a solid cylinder, we find:
$6 = (.31+\frac{1}{2}M(.15)^2)(7.33) $
$M = 45.2 \ kg$
*Note, we set this equal to 6 since the angular momentum changes from 3 to -3, which is a change of 6.
