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Conservation of angular momentum is a fundamental principle in physics, stating that if no external torque acts on a system, the total angular momentum of that system remains constant. In simpler terms, an object's spin will not change unless something causes it to. This principle is crucial in understanding the behavior of objects in rotational motion, such as stars, planets, and even galaxies.

For instance, in the exercise provided, a star collapses into a neutron star. Despite its significant change in size, if the system is isolated (meaning no external forces or moments act upon it), the star's angular momentum before and after the collapse must be identical. This conservation underpins the calculation to find the angular speed of the neutron star post-collapse. The process takes into account the star's initial rotation rate and adjusts it based on changes in the star's moment of inertia due to the collapse.

Understanding the law of conservation of angular momentum helps us comprehend how different bodies in space can change their rotational speeds after events such as supernovae or collisions, which can alter their distribution of mass.

Neutron stars are incredibly dense, the density being roughly a colossal amount of times greater than that of ordinary solid matter. This extreme density means that a tremendous amount of mass is packed into a very small volume. A neutron star's density arises from its formation process; when a massive star ends its life cycle, it can go supernova, ejecting its outer layers. What remains collapses under gravity to an almost point-like object, leaving behind a neutron star.

The density of a neutron star is such that a teaspoonful of its material would weigh about a billion tons on Earth. This supreme compactness drastically increases the star's mass per unit volume (density), which, along with its radius, affects the star's moment of inertia – a key factor when calculating changes in angular speed as seen in the textbook exercise. The exercise involves using the concept of density to understand the scale of the physical changes a star undergoes when it collapses into a neutron star.

The moment of inertia is a measure of an object's resistance to changes in its rotation about an axis. It is an important concept, especially when dealing with rotational motion in physics. The moment of inertia is dependent on the object's mass and how that mass is distributed relative to the axis of rotation.

In our cosmic example involving a neutron star, we use the formula for the moment of inertia of a sphere, given by \( I = \frac{2}{5}mr^2 \) where \( m \) is the mass and \( r \) is the radius. Before and after the collapse of the star into a neutron star, the moments of inertia change dramatically due to the vast differences in their radii.

This change in the moment of inertia is key to solving for the angular speed after the collapse. The moment of inertia is inversely proportional to the angular speed, following the conservation of angular momentum. Therefore, as a star collapses and its moment of inertia decreases (due to a decrease in radius), its angular speed increases, resulting in a faster spinning neutron star, as calculated in the exercise.