What is the angular momentum of earth?

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Answer 1 · 2018-05-08T00:49:11

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)

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

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.