A plane fires its thrusters in order to make itself spin at 1.2 rad/s. Then, it unlocks its solar panels, allowing them to extend. After the extension of the solar panels, the plane's moment of inertia is 14 kg-m2, and its angular velocity is 0.77 rad/s.

There is no torque exerted on the plane while the solar panels extend.

What was the moment of inertia before the solar panels were unlocked and allowed to extend?

Question

25-12-2023
Physics

High School

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A plane fires its thrusters in order to make itself spin at 1.2 rad/s. Then, it unlocks its solar panels, allowing them to extend. After the extension of the solar panels, the plane's moment of inertia is 14 kg-m2, and its angular velocity is 0.77 rad/s.

There is no torque exerted on the plane while the solar panels extend.

What was the moment of inertia before the solar panels were unlocked and allowed to extend?

Answer :

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sbitane986 sbitane986 · Answer 1 · 2023-10-04T05:09:39-04:00

The moment of inertia before the solar panels were unlocked and allowed to extend is [tex]9.07 kg-m^2.[/tex] by the using of principle of conservation of angular momentum.

The initial angular momentum of the plane is equal to the final angular momentum after the solar panels extend.

The formula for angular momentum is given by L = I * ω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

Given that the plane's initial angular velocity is 1.2 rad/s and its moment of inertia after the extension is [tex]14 kg-m^2[/tex] with an angular velocity of 0.77 rad/s, we can set up the equation:

I_initial * ω_initial = I_final * ω_final

Let's solve for I_initial:

I_initial = (I_final * ω_final) / ω_initial

Substituting the values, we have:

I_initial = ([tex]14 kg-m^2[/tex] * 0.77 rad/s) / 1.2 rad/s

I_initial = [tex]9.0667 kg-m^2[/tex]

The moment of inertia before the solar panels were unlocked and allowed to extend is approximately [tex]9.07 kg-m^2.[/tex]

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