Hi there!
We can use the conservation of angular momentum to solve.
[tex]L_i = L_f\\\\I\omega_i = I\omega_f[/tex]
I = moment of inertia (kgm²)
ω = angular velocity (rad/sec)
Recall the following equations for the moment of inertia.
[tex]\text{Solid cylinder:} I = \frac{1}{2}MR^2\\\\\text{Object around center:} = MR^2[/tex]
Begin by converting rev/sec to rad sec:
[tex]\frac{0.17rev}{s} * \frac{2\pi rad}{1 rev} = 1.068 \frac{rad}{s}[/tex]
According to the above and the given information, we can write an equation and solve for ωf.
[tex]1.068(\frac{1}{2}(34)(1.6)^2 + (79)(1.6)^2) = \omega_f(\frac{1}{2}(34)(1.6^2) + 79(0^2))\\\\\omega_f = \boxed{6.03 \frac{rad}{sec}}[/tex]
