Question

a) Calculate the angular momentum of Earth that arises from its spinning motion on its axis, treating Earth as a uniform solid sphere. J · s (b) Calculate the angular momentum of Earth that arises from its orbital motion about the Sun, treating Earth as a point particle. J · s

Answer 1

Angular momentum is given by:

L = I*w

a.)

here, I = moment of inertia about its center axis = (2/5)*Me*Re^2

where, Me = mass of earth = 5.97*10^24 kg

Re = radius of earth = 6.371*10^6 m

w = angular speed = (1 rev/24 hr)(1 hr/3600 s)(2*pi/1 rev) = 7.272*10^-5 rad/s

So,

Angular momentum = L = I*w = (2/5)*Me*Re^2*w

L = 2*5.98*10^24*(6.371*10^6)^2*7.272*10^-5/5

L = 7.06*10^33 J-sec

b.)

now moment of inertia about sun is given by,

Is = I + Me*R^2

here, R = distance from sun = 1.496*10^11 m

So, Is = [(2/5)(5.97*10^24)(6.371*10^6)^2 + (5.97*10^24)*(1.496*10^11)^2]

Is = 1.336*10^47 kg*m^2

w' =  (1 rev/365 day)(1 days/(24*3600) s)(2*pi/1 rev)

w' = 1.991*10^-7 rad/s

So, Now angular momentum will be:

L = Is*w'

L = 1.336*10^47*1.991*10^-7

L = 2.66*10^40 J-sec

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