A solid sphere of radius r rotates about a diameter with an angular speed w. the sphere then collapses under the action of inter
2 answers:
The final angular speed of the sphere is 4ω.
<h3>Calculation:</h3>Angular momentum will remain conserved.
<h3>What is conservation of angular momentum?</h3>A spinning system's ability to conserve angular momentum ensures that its spin will not change until it is subjected to an external torque; in other words, the rotation's speed will not change as long as the net torque is zero.
Angular momentum is given by,
L = Iω
where,
L = angular momentum
I = moment of inertia
ω = angular speed
The moment of inertia of a solid sphere is,
I =
For the question,
L₁ = L₂
I₁ω₁ = I₂ω₂
Given,
R₁ = R
R₂ = R/2
ω₁ = ω
To find,
ω₂ =?
Substituting the values in the equation,
I₁ω₁ = I₂ω₂
(MR²)ω =
M(R/2)²ω₂
R²ω = (R²/4)ω₂
ω = (1/4)ω₂
ω₂ = 4ω
Hence, the final angular speed of the sphere is 4ω.
Learn more about conservation of angular momentum here:
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4ω is the final angular speed of the sphere.
When a solid sphere of radius r rotates about a diameter with an angular speed w, the sphere then collapses under the action of internal forces to a final radius r/2, 4ω is the final angular speed of the sphere.
Angular momentum will remain conserved.
Angular momentum is given by,
L = Iω
where,
L = angular momentum
I = moment of inertia
ω = angular speed
The moment of inertia of a solid sphere is,
I =
For the given problem,
L₁ = L₂
I₁ω₁ = I₂ω₂
We are given,
R₁ = R
R₂ = R/2
ω₁ = ω
To find,
ω₂ =?
On substitution of the values in the equation,
I₁ω₁ = I₂ω₂
(MR²)ω =
M(R/2)²ω₂
R²ω = (R²/4)ω₂
ω = (1/4)ω₂
ω₂ = 4ω
Hence, we can conclude that the final angular speed of the sphere is 4ω.
To learn more about conservation of angular momentum visit:
#SPJ4
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