Answer:
[tex]\omega_{f} \approx 47.659\,\frac{rad}{s}\,(7.585\,\frac{rev}{s} )[/tex]
Explanation:
The diver can be modelled by using the Principle of Angular Moment Conservation:
[tex]I_{o}\cdot \omega_{o} = I_{f}\cdot \omega_{f}[/tex]
The final angular velocity is:
[tex]\omega_{f} = \frac{I_{o}}{I_{f}}\cdot \omega_{o}[/tex]
[tex]\omega_{f} = \frac{\frac{1}{12}\cdot m\cdot L^{2} }{\frac{2}{5}\cdot m \cdot R^{2} }\cdot \omega_{o}[/tex]
[tex]\omega_{f} = \frac{5\cdot L^{2}}{24\cdot R^{2}} \cdot \omega_{o}[/tex]
Let assume that L = 1.60 m and R = 0.15 m.
[tex]\omega_{f} = \frac{5\cdot (1.60\,m)^{2}}{24\cdot (0.15\,m)^{2}}\cdot (0.32\,\frac{rev}{s} )\cdot (\frac{2\pi\,rad}{1\,rev} )[/tex]
[tex]\omega_{f} \approx 47.659\,\frac{rad}{s}\,(7.585\,\frac{rev}{s} )[/tex]
