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

a)

The angular momentum of Earth can be obtained by

$L = I \omega$

Where

I = moment of inertia of a sphere (as Earth is considered a sphere) = 2/5 mr²

$\omega$ = angular velocity = $2\pi / 1 day = 2 \pi / (24 *3600)$ ( as 1 day as 24 hours and each hour has 3600 s)

So,

L = 2/5 mr² x $2 \pi / (24 *3600)$

m = mass of earth = 5.97 x 10²⁴ kg

r = radius of earth = 6.38 x 10⁶ m

So, L = 2/5 x (  5.97 x 10²⁴ x (6.38 x 10⁶)² ) x $2 \pi / (24 *3600)$ Js

So, L = 7.07 x 10³³ Js-----------------(Answer)

b)

We will use the same expression for angular momentum but in this case

I = moment of inertia = mr²

$\omega$ = angular velocity = $2\pi / 365 days = 2 \pi / (365 *24 *3600)$ ( as revolution time is 365 days and 1 day has 24 hours and each hour has 3600 s)

So,

L = mr² x $2 \pi / (365 *24 *3600)$

m = mass of earth = 5.97 x 10²⁴ kg

r = radius of orbit = 1.5 x 10¹¹ m

So, L = (  5.97 x 10²⁴ x (6.38 x 10⁶)² ) x $2 \pi / (365 *24 *3600)$ Js

So, L = 2.676 x 10⁴⁰ Js----------------(Answer)