Rotaty motion

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

Correct answer:

v =  2.6458 m/s
f =  0.6015 Hz

Step-by-step explanation:

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

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

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