What is the moment of inertia of the earth?

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What is the moment of inertia of the earth?

Given that the radius of the earth is $6.38 \times 10^{6} m$ $6.38xx10^6"m"$ and the mass of the earth is $5.98 \times 10^{24} kg$ $5.98xx10^24"kg"$ .

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Answer 1 · 2017-08-15T04:15:38

$I \approx 9.736 \times 10^{37} {kgm}^{2}$ $I~~9.736xx10^37"kgm"^2$

Explanation:

If we think of the earth as a solid sphere rotating about its center, the moment of inertia is given by:

$I = \frac{2}{5} M R^{2}$ $color(darkblue)(I=2/5MR^2)$

where $M$ $M$ is the mass of the earth and $R$ $R$ is its radius

We are given the following information:

$\mapsto M = 5.98 \times 10^{24} kg$ $|->M=5.98xx10^24"kg"$
$\mapsto R = 6.38 \times 10^{6} m$ $|->R=6.38xx10^6"m"$

Substituting these values into the equation above:

$I = \frac{2}{5} (5.98 \times 10^{24} kg) {(6.38 \times 10^{6} m)}^{2}$ $I=2/5(5.98xx10^24"kg")(6.38xx10^6"m")^2$

$\Rightarrow = \frac{2}{5} (5.98 \times 10^{24} kg) (4.07044 \times 10^{13} m^{2})$ $=>=2/5(5.98xx10^24"kg")(4.07044xx10^13"m"^2)$

$\Rightarrow \frac{2}{5} (2.4341 \times 10^{38} {kgm}^{2})$ $=>2/5(2.4341xx10^38"kgm"^2)$

$\Rightarrow = 9.736 \times 10^{37} {kgm}^{2}$ $=>color(darkblue)(=9.736xx10^37"kgm"^2)$

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What is the moment of inertia of the earth?

Given that the radius of the earth is $6.38 \times 10^{6} m$ $6.38xx10^6"m"$ and the mass of the earth is $5.98 \times 10^{24} kg$ $5.98xx10^24"kg"$ .

1 Answer

Explanation:

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Science

Math

Humanities

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What is the moment of inertia of the earth?

Given that the radius of the earth is 6.38xx10^6"m"6.38×106m6.38xx10^6"m" and the mass of the earth is 5.98xx10^24"kg"5.98×1024kg5.98xx10^24"kg".

1 Answer

Explanation:

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Impact of this question

Given that the radius of the earth is $6.38 \times 10^{6} m$ $6.38xx10^6"m"$ and the mass of the earth is $5.98 \times 10^{24} kg$ $5.98xx10^24"kg"$ .