Calculate the angular momentum of the spherical earth rotating about its own axis, if the mass of earth =5.98*10^24 kg and mean radius of the earth =6.38*10^6m.
Answers
Answer:
The angular momentum due to the earth's rotation is
≈
7.2
×
10
33
Kg
m
2
s
−
1
(this value is with respect to a co-moving observer)
Explanation:
can estimate the angular momentum due to the earth's rotation by approximating the earth by a uniform sphere of
mass
M
=
6.0
×
10
24
Kg
and
radius
R
=
6.4
×
10
6
m
The moment of inertia of a uniform solid sphere about any axis passing through the center is
I
=
2
5
M
R
2
and so, for the earth it is
I
=
2
5
×
6.0
×
10
24
×
(
6.4
×
10
6
)
2
Kg
m
2
=
≈
9.8
×
10
37
Kg
m
2
The earth's angular velocity is
ω
=
2
π
1
day
=
2
π
24
×
60
×
60
s
−
1
≈
7.3
×
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
ω
≈
7.2
×
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.
Answer:
Please refer to the Attachment
Hope that helps !
