Answer
.33 radians per second
Work Step by Step
We find:
$\omega_{bird} = \frac{I\omega_1-m_bv_bR}{I+m_{bird}R^2}$
$\omega_{bird} = \frac{(.12)(.586)-(.14)(1.1)(.19)}{.12+(.14)(.19)^2}\approx \fbox{.33 radians per second}$
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