## Essential University Physics: Volume 1 (3rd Edition)

a) $\omega_f=2.5 \ rads/s$ b) $W=3.4 \times 10^{-3}J$
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: $W=3.4 \times 10^{-3}J$