Rank the following hypothetical planets -- all of which have the same total mass and same radius -- from lowest moment of inertia to highest moment of inertia:
1) A uniform sphere of mixed up rock and iron
2) A rocky planet with an iron core
3) A rocky planet with an iron crust
4) A uranium planet with a thick atmosphere (where the radius is measured to the top of the atmosphere)
Well, let's see. Moment of inertia is the measure of an object's resistance to changes in rotational motion. So, let's clown around with these planets:
In terms of moment of inertia, let's rank these planets from lowest to highest.
Coming in at number 1, we have the uranium planet with a thick atmosphere. It's going to have a pretty low moment of inertia because uranium is dense and heavy. Plus, with all that thick atmosphere, it's going to create some extra drag, making it easier to spin. It's like trying to juggle bowling balls in a rainstorm!
Next up at number 2, we have the uniform sphere of mixed-up rock and iron. This one will have a bit higher moment of inertia because the mixing of materials will distribute the mass more evenly. It's like trying to juggle a bunch of different-sized balls - it takes a little more effort to keep them all in the air.
Moving on to number 3, we have the rocky planet with an iron crust. The iron crust will give it a slightly higher moment of inertia compared to the uniform sphere. It's like trying to juggle eggs and bowling balls at the same time - you'll have to adjust your juggling technique a bit.
Finally, at number 4, we have the rocky planet with an iron core. With the denser iron core concentrated at the center, this one will have the highest moment of inertia. It's like trying to juggle a bunch of rocks covered in feathers - it's going to take some serious skill and strength to keep them all in the air.
So, there you have it, from low to high moment of inertia, we have the uranium planet, the uniform sphere of mixed-up rock and iron, the rocky planet with an iron crust, and finally, the rocky planet with an iron core.
To rank the hypothetical planets from lowest moment of inertia to highest moment of inertia, we need to consider the distribution of mass within each planet. The moment of inertia depends on how mass is distributed in an object. Objects with mass concentrated further from the center have higher moments of inertia.
1) Rocky planet with an iron crust: This type of planet would have a lower moment of inertia compared to the others because the iron is concentrated towards the outer layer, closer to the surface, resulting in less mass distributed further from the center.
2) A uniform sphere of mixed up rock and iron: This planet would have a higher moment of inertia compared to the first one because the rock and iron would be evenly distributed throughout the entire planet, including towards the center.
3) A rocky planet with an iron core: This type of planet would have a higher moment of inertia compared to the second one because the heavier iron core would cause more mass to be distributed further from the center.
4) Uranium planet with a thick atmosphere: This planet would have the highest moment of inertia among the listed options. Uranium is a dense element, and having a thick atmosphere would result in a significant amount of mass distributed further from the planet's center.
Therefore, the ranking from lowest moment of inertia to highest moment of inertia would be:
1) A rocky planet with an iron crust
2) A uniform sphere of mixed up rock and iron
3) A rocky planet with an iron core
4) A uranium planet with a thick atmosphere
To rank the hypothetical planets based on their moment of inertia, we need to understand the concept of moment of inertia and how it relates to the distribution of mass within an object.
Moment of inertia is a measure of an object's resistance to rotational motion around a particular axis. It depends on both the mass and the distribution of that mass within the object. The moment of inertia tends to be lower for masses concentrated closer to the axis of rotation and higher for masses distributed farther from the axis.
Now let's analyze each planet scenario to determine their moment of inertia:
1) A uniform sphere of mixed up rock and iron:
In this case, the mass is evenly distributed throughout the sphere. Since the density of rock and iron is fairly similar, the mass distribution won't vary significantly. Therefore, the moment of inertia of this planet would be relatively high, but not the highest due to the presence of mixed mass and the uniform distribution throughout.
2) A rocky planet with an iron core:
In this scenario, the planet has a rocky outer layer and a dense iron core. The core, being denser, would have a higher mass compared to the outer layers. Consequently, the moment of inertia would be lower than scenario 1 because more mass is concentrated closer to the core's axis of rotation.
3) A rocky planet with an iron crust:
This planet possesses an iron crust, which means more mass is concentrated toward the outer layers compared to the core. The moment of inertia would be higher than scenario 2 but lower than scenario 1 because the significant mass of the core is further from the axis of rotation.
4) A uranium planet with a thick atmosphere:
In this scenario, the planet is composed mainly of uranium, which has a higher density compared to rock and iron. Additionally, the thick atmosphere indicates more mass distributed farther from the axis of rotation. The moment of inertia of this planet would be the highest among the given scenarios because both the uranium core and the thick atmosphere contribute to the mass distribution, which is further from the axis of rotation.
Based on this analysis, the ranking of the hypothetical planets from lowest to highest moment of inertia would be:
2) A rocky planet with an iron core
3) A rocky planet with an iron crust
1) A uniform sphere of mixed up rock and iron
4) A uranium planet with a thick atmosphere