What does it mean to say that angular momentum is conserved? Give an example of what you might see on Earth. How could conservation of angular momentum help astronomers understand the development of the solar system?

When we say that angular momentum is conserved, it means that the total angular momentum of a system remains constant over time, provided no external torques act on it. In simpler terms, it implies that the spinning or rotating motion of an object or a system will remain unchanged unless some external force is applied.

To understand this concept, let's consider an example on Earth. Imagine a figure skater performing a spin. Initially, the skater has her arms extended outward. As she pulls her arms closer to her body, her rotational speed, or angular velocity, increases. This change in the skater's rotational motion is a result of the conservation of angular momentum. By pulling her arms closer, she reduces her moment of inertia (a measure of an object's resistance to changes in rotation), leading to an increase in angular velocity to maintain the same overall angular momentum.

Now let's explore how conservation of angular momentum can aid astronomers in understanding the development of the solar system. According to the nebular hypothesis, which is widely accepted, the solar system formed from a spinning cloud of gas and dust known as the solar nebula. As the nebula collapsed under its own gravity, it began to spin faster due to the conservation of angular momentum.

As the cloud gradually contracted, the conservation of angular momentum caused it to spin faster, much like the figure skater pulling her arms closer. This increased rotation led to the formation of a protoplanetary disk, where individual particles gradually combined to form planets, asteroids, and other celestial objects. This understanding of angular momentum conservation helps astronomers explain why planets generally orbit in the same direction and lie in a roughly flat plane around the Sun.

By studying the distribution of angular momentum in different regions of the solar system, astronomers can gain insights into the early stages of planet formation and the dynamical processes that shaped our solar system. Conservation of angular momentum is a fundamental principle that underlies our understanding of rotational motion in various systems, from figure skaters to the cosmos.