Answer
2.088 radians per second
Work Step by Step
In order to solve this problem, we first need to find the torque:
$\tau = Fr =75 \times .45 = 33.75 \ Nm$
We now find the moment of inertia:
$ I = \frac{1}{2} mr^2 = \frac{1}{2} (120)(.45)^2 =12.15 \ kgm^2$
Thus, we find the final angular velocity:
$ \omega_f =\sqrt{\frac{2\tau\theta}{I}}=\sqrt{\frac{2(33.75 \ Nm)(.785 \ rads)}{12.15 \ kgm^2}}=\fbox{2.088 radians per second}$
