Question

How can the concepts of conservation of energy and momentum be applied to determine how the temperature and rotation rates of celestial objects change as their sizes change?

Answer 1

Celestial objects such as star have rotational inertia along with angular momentum and rotational kinetic energy. As size of star changes preferably decreasing its angular momentum remains constant while angular velocity increases. Some rotational kinetic energy gets transformed to this increased angular velocity while some in increase in temperature of the star . So initial rotational kinetic energy is equal to sum of final rotational kinetic energy and internal energy which associated with rise in temperature.