# 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?

Result

v =  2.646 m/s
f =  0.602 Hz

#### Solution:

$r=70 \ cm=70 / 100 \ m=0.7 \ m \ \\ g=10 \ \text{m/s}^2 \ \\ F_g=F_o \ \\ m g=\dfrac{ mv^2 }{ r } \ \\ g=\dfrac{ v^2 }{ r } \ \\ \ \\ v=\sqrt{ r \cdot \ g }=\sqrt{ 0.7 \cdot \ 10 } \doteq \sqrt{ 7 } \doteq 2.6458 \doteq 2.646 \ \text{m/s} \ \\ \ \\ ω=v/r=2.6458/0.7 \doteq 3.7796 \ 1\text{/rad}$
$ω=2 \ \pi f \ \\ \ \\ f=\dfrac{ ω }{ 2 \pi }=\dfrac{ 3.7796 }{ 2 \cdot \ 3.1416 } \doteq 0.6015 \doteq 0.602 \ \text{Hz}$

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