Rotaty motion

What is the minimum speed and frequency that we need to rotate with water can in a vertical plane along a circle with a radius of 70 cm to prevent water from spilling?

Correct result:

v =  2.6458 m/s
f =  0.6015 Hz

Solution:

$$\begin{gathered} r=70\text{ cm}\to \text{ m}=70\mathrm{/}100\text{ m}=0.7\text{ m } \\ g=10{\text{m/s}}^2 \\ {F}_g=F_o \\ mg={\displaystyle \frac{m{v}^2}{r}} \\ g={\displaystyle \frac{v^2}{r}} \\ v=\sqrt{r\cdot g}=\sqrt{0.7\cdot 10}=\sqrt{7}\doteq 2.6458=2.6458\text{ m/s } \\ \omega =v\mathrm{/}r=2.6458\mathrm{/}0.7\doteq 3.77961\text{/rad} \end{gathered}$$

$$\begin{gathered} \omega =2\pi f \\ f={\displaystyle \frac{\omega }{2\pi }}={\displaystyle \frac{3.7796}{2\cdot 3.1416}}=0.6015\text{ Hz} \end{gathered}$$

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