Answer:
5.82812 rad/s
Explanation:
L = Length of meter stick = 1 m = 100 cm
[tex]m_c[/tex] = The center of mass of the stick = [tex]\frac{L}{2}-0.22=0.5-0.22=0.28\ m[/tex]
[tex]\omega[/tex] = Angular velocity
Moment of inertia of the system is given by
[tex]I=I_c+mr^2\\\Rightarrow I=\frac{mL^2}{12}+mr^2\\\Rightarrow I=\frac{m1^2}{12}+m0.28^2\\\Rightarrow I=m(\frac{1}{12}+0.0784)[/tex]
As the energy in the system is conserved
[tex]mgh=I\frac{\omega^2}{2}\\\Rightarrow mgh=m(\frac{1}{12}+0.0784)\frac{\omega^2}{2}\\\Rightarrow gh=(\frac{1}{12}+0.0784)\frac{\omega^2}{2}\\\Rightarrow \omega=\sqrt{\frac{2gh}{\frac{1}{12}+0.0784}}\\\Rightarrow \omega=\sqrt{\frac{2\times 9.81\times 0.28}{\frac{1}{12}+0.0784}}\\\Rightarrow \omega=5.82812\ rad/s[/tex]
The maximum angular velocity is 5.82812 rad/s
