Given data
The magnitude of the total force is F = 210 N
The mass of the rock is m = 0.23 kg
The length of the string is L = 0.35 m
The expression for the maximum angualr velocity is given as:
[tex]\begin{gathered} F=m\omega^2L \\ \omega=\sqrt{\frac{F}{mL}} \end{gathered}[/tex]Substitute the value in the above equation.
[tex]\begin{gathered} \omega=\sqrt[]{\frac{210\text{ N}}{0.23\text{ kg }\times\text{0.35 m}}} \\ \omega=51.07\text{ rad/s} \end{gathered}[/tex]Thus, the maximum angular velocity of the rock is 51.07 rad/s.
