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 moment L = I ω
Moment of inertia I = [2/5]mr^2 and angular velocity ω = 2π/T =[ 2π/86400] rad/s
mass m = 5.978e24kg, radius r = 6.378e6m
=> L = [2/5]*5.978*10^24* 6.378*10^6*6.378*10^6*[ 2π/86400]
=> L = 7.07*10^33 kg.m^2S^-1.

b) For orbital motion of earth about the sun
I = m R^2 where R is the orbital radius.
T = 1 year = 3.154*10^7 s
ω = 2π/T = 2π/T = 2π/3.154*10^7s = 1.99*10^-7rad/s
L = I ω. = (5.978e24)*(6.378*10^6)^2*1.99e-7
L = 4.84*10^29 kg.m^2s^-1.