A spaceship fires its thrusters in order to make itself spin at 1.2rad/s. Then, it unlocks its solar panels, allowing them to extend. After the extension of the solar panels, the spaceship's moment of inertia is 14 kg−m2, and its angular velocity is 0.77rad/s. There is no torque exerted on the spaceship while the solar panels extend. What was the moment of inertia before the solar panels were unlocked and allowed to extend?

When the spaceship fires its thrusters to spin at 1.2 rad/s, it experiences an angular acceleration. This means that a torque is applied to the spaceship, causing it to change its rotational motion. The torque is given by the equation:

Torque = Moment of Inertia * Angular Acceleration

After the solar panels are unlocked and allowed to extend, there is no torque exerted on the spaceship. This means that the angular acceleration becomes zero. We can use this information to solve for the moment of inertia before the solar panels were unlocked.

Using the equation:

Angular Acceleration = (Final Angular Velocity - Initial Angular Velocity) / Time

Since the angular acceleration is zero, we have:

0 = (0.77 rad/s - 1.2 rad/s) / Time

Simplifying the equation, we find:

Time = (0.77 rad/s - 1.2 rad/s) / 0

Since the time is zero, it means that the angular velocity remains constant throughout the extension of the solar panels. Therefore, we can equate the moment of inertia before and after the extension:

Moment of Inertia * Initial Angular Velocity = Moment of Inertia * Final Angular Velocity

Solving for the moment of inertia before the extension, we get:

Moment of Inertia before = (Moment of Inertia after * Final Angular Velocity) / Initial Angular Velocity

= (14 kg−m2 * 0.77 rad/s) / 1.2 rad/s

≈ 20 kg−m2

Therefore, the moment of inertia before the solar panels were unlocked and allowed to extend was approximately 20 kg−m2.

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