Question

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. what is the final angular speed of the sphere

Answer 1

The final angular speed of the sphere is 4ω.

Calculation:

Angular momentum will remain conserved.

What is conservation of angular momentum?

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 = $\frac{2}{5} MR^{2}$

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

$\frac{2}{5}$(MR²)ω = $\frac{2}{5}$ 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:

brainly.com/question/12998770

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Answer 2

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 = $\frac{2}{5}$$MR^{2}$

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

$\frac{2}{5}$(MR²)ω = $\frac{2}{5}$ 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:

brainly.com/question/1597483

#SPJ4