Momentum
Beginner
Conservation of Angular Momentum
Source: High school physics (Chinese)
Problem Sets:
momentum -1112
Problem
The Moon's orbit around the Earth can be approximated as a circle. The Earth's mass is $M_e$, the Moon's mass is $M_m$, and the distance between them is $r_0$.
Find the angular momentum of the Moon with respect to the Earth's center.
$L = M_m \sqrt{G M_e r_0}$
The gravitational force provides the centripetal force for the Moon's circular orbit.
$$F_g = F_c \implies G \frac{M_e M_m}{r_0^2} = M_m \frac{v^2}{r_0}$$Solving for the orbital speed $v$:
$$v = \sqrt{\frac{G M_e}{r_0}}$$The angular momentum $L$ of the Moon is $L = M_m v r_0$. Substituting the expression for $v$:
$$L = M_m r_0 \sqrt{\frac{G M_e}{r_0}} = M_m \sqrt{G M_e r_0}$$