Question

how to calculate the angular momentum of the earth rotating about its own axis.radius of the earth is 6.37*10to the power6m and mass of the earth

is 5.98*10 to the power 27kg

Answer 1

Angular velocity of Earth
ω = 2 π / T
= 2 π / (86400) ……[∵ It takes 24 hrs (=86400 s) to complete one full rotation]
= 7.26 × 10⁻⁵ rad/s

Moment of inertia of earth
I = 0.4 mR²
= 0.4 × 5.98 × 10²⁷ × (6.37 × 10⁶)²
= 9.70 × 10⁴⁰ kgm²

Angular Momentum = Moment of inertia × Angular velocity
= 9.70 × 10⁴⁰ × 7.26 × 10⁻⁵
= 7.0 × 10³⁶ kgm²/s

Angular momentum of earth is 7.0 × 10³⁶ kgm²/s

Answer 2

Answer:

For earth we have moment of inertia as

I=  

5

2

​  

mR  

2

 

and angular velocity as

ω=  

T

2π

​  

 

Thus angular momentum is given as

L=  

5

2

​  

mR  

2

×  

T

2π

​  

 

Substituting the values of the parameters

L=  

5

2

​  

(5.978×10  

24

kg)(6.378×10  

6

m)  

2

×  

86400s

2π

​  

or

L=7×10  ^33  kg/m ^ 2 /sec