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"#.

1 Answer
Aug 15, 2017

Answer:

#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)#