Subsection 3.2.6 Principle of Conservation of Angular Momentum
Conservation of angular momentum tells that in rotaiton, initial angular momentum is always equal to final angular momentum of the body if no external torque is acting on it. That is
\begin{align}
L_1 \amp =L_2\tag{3.2.9}\\
or, \quad I_1\omega_1 \amp = I_2\omega_2\tag{3.2.10}\\
or, \quad m_1v_1r_1 \amp = m_2v_2r_2\tag{3.2.11}
\end{align}
If the moment of inertia of a rotaing body decreases then rotational velocity is going to increase. For example: 1. when ice skaters spin by pulling their arms inwards their rotational speed increase but their rotational speed decrease when they stretched their arms outwards. 2. A system of planets orbiting around a star has no net external torque acting, so its angular momentum is constant. Hence, when a planet travels along an elliptical orbit, its speed reduces when it is further away from the star and its speed increases as it approaches the star star-planet system. Look at the planetary motion of Nereid (Naptune’s moon) in the law of orbits animation.
3
physics.weber.edu/amiri/director-dcrversion/newversion/kepler/Kepler_1.2.html
