Question

Earth has a mass of 5.97 * 10^24 kg and a radius of 6.38 *10^6 m. Assume it is a uniform solid sphere. The distance of Earth from the Sun is 1.50 * 10^11 m. (Assume Earth completes a single rotation in 24.0 hours and orbits the Sun once every 365 Earth days.)

(a) Calculate the angular momentum of Earth in its orbit around the Sun.

(b) Calculate the angular momentum of Earth on its axis.

Please show your work.

Answer 1

a)

m = 5.97 * 10^24 Kg

r = 6.38 *10^6 m

angular momentum of earth around sun = m * v * r

angular momentum of earth around sun = m * r^2 * w

angular momentum of earth around sun = 5.97 * 10^24 * (1.5 *10^11)^2 * (2pi/(365 * 24 * 3600))

angular momentum of earth around sun = 2.677 * 10⁴⁰ Kg.m^2/s

b)

angular momentum of Earth on its axis = I * w

angular momentum of Earth on its axis = 2/5 * m * r^2 * w

angular momentum of Earth on its axis = 2/5 * 5.97 *10^24 * (6.38 *10^6)^2 * 2pi/(24 * 3600)

angular momentum of Earth on its axis = 7.07 * 10^33 Kg.m^2/s