The oscillation angular frequency of a drop with half of the first drop's radius is 4ω
<h3>What is surface tension?</h3>
Surface tension is the tension force exerted on an object by the surface of a liquid.
<h3>What is angular frequency?</h3>
Angular frequency is the frequency of oscillation of a rotating object. It is given in rad/s.
<h3>What is the oscillation angular frequency of a drop with half of the first drop's radius?</h3>
Given that
- the angular frequency of the drop is ω and
- radius r.
Since the energy of the drop is conserved, using the law of conservation of angular momentum, we have
Iω = I'ω' where
- I = initial rotational inertia of droplet = mr²
- where m = mass of drop and
- r = initial radius of droplet,
- ω = initial angular frequency of droplet,
- I' = initial rotational inertia of droplet = mr² where
- m = mass of drop and
- r' = final radius of droplet, and
- ω = final angular frequency of droplet
So, Iω = I'ω'
Making ω' subject of the formula, we have
ω' = Iω/I'
ω' = mr²ω/mr'²
ω' = r²ω/r'²
Given that the drop is half of the first drop's radius, r' = r/2
So, ω' = r²ω/r'²
ω' = r²ω/(r/2)²
ω' = r²ω/r²/4
ω' = 4ω
So, the oscillation angular frequency of a drop with half of the first drop's radius is 4ω
Learn more about angular frequency here:
brainly.com/question/28036464
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