What is the angular momentum of earth?

1 Answer
May 8, 2018

Answer:

The angular momentum due to the earth's rotation is #~~7.2times 10^33\ "Kg"\ "m"^2"s"^-1#
(this value is with respect to a co-moving observer)

Explanation:

We can estimate the angular momentum due to the earth's rotation by approximating the earth by a uniform sphere of

  • mass #M= 6.0times 10^24\ "Kg"# and
  • radius #R = 6.4 times 10^6\ "m"#

The moment of inertia of a uniform solid sphere about any axis passing through the center is

#I = 2/5MR^2#

and so, for the earth it is

#I = 2/5 times 6.0 times 10^24times (6.4times 10^6)^2\ "Kg"\ "m"^2#
#quad = ~~9.8times 10^37\ "Kg"\ "m"^2#

The earth's angular velocity is

#omega = (2 pi)/(1\ "day") = (2pi)/(24times 60times 60)\ "s"^-1~~7.3times 10^-5\ "s"^-1#

So, the angular momentum of the earth's rotation (with respect to an observer co-moving with it) is

#L = I omega ~~7.2times 10^33\ "Kg"\ "m"^2"s"^-1#

Note that

  • the angular momentum due to the revolution of the earth (with respect to the sun)is much larger than this.
  • since the earth actually has a dense inner core, the actual moment of inertia is smaller than that estimated here.