Question

What is the moment of inertia of the earth?

Given that the radius of the earth is `6.38xx10^6"m"` and the mass of the earth is `5.98xx10^24"kg"`.

Answer 1

`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:

`color(darkblue)(I=2/5MR^2)`

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

We are given the following information:

• `|->M=5.98xx10^24"kg"`
• `|->R=6.38xx10^6"m"`

Substituting these values into the equation above:

`I=2/5(5.98xx10^24"kg")(6.38xx10^6"m")^2`

`=>=2/5(5.98xx10^24"kg")(4.07044xx10^13"m"^2)`

`=>2/5(2.4341xx10^38"kgm"^2)`

`=>color(darkblue)(=9.736xx10^37"kgm"^2)`