Answer
a) $ \omega_f=2.5 \ rads/s$
b) $W=3.4 \times 10^{-3}J$
Work Step by Step
a) We know that angular momentum is conserved. Since the old angular speed was 2.3 radians per second, we use the new moment of inertia to find the new angular speed:
$L_0=L_f \\ I\omega_f = I\omega_0 + m\omega_0r^2 \\ .0154\omega_f=.0154(2.3)+(.0195)(2.3)(.25)^2 \\ \omega_f=2.5 \ rads/s$
b) Thus, we can find the work done by finding the change in energy:
$W = \frac{1}{2}I\omega_f^2 -\frac{1}{2}I\omega_0^2+\frac{1}{2}mr^2\omega_0$
Plugging in the known values, we find:
$W=3.4 \times 10^{-3}J$
