Question

What is the angular momentum of earth?

Answer 1

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.