The centripetal force felt by the trainer on her back its equal to 7.25 times its weight, therefore:
[tex]F_c=7.25W\\F_c=7.25(mg)[/tex]
The centripetal force is given by:
[tex]F_c=ma_c=m\frac{v^2}{r}=m\omega^2 r[/tex]
Replacing this and solving for the angular speed, we have:
[tex]m\omega^2 r=7.25mg\\\omega^2=\frac{7.25g}{r}\\\omega=\sqrt{\frac{7.25g}{r}}\\\omega=\sqrt{\frac{7.25*9.8\frac{m}{s^2}}{11m}}\\\omega=2.54\frac{rad}{s}[/tex]
