tion of dizziness. You feel absolutely queasy, and need to sit down on a nearby bench.
Just as linear motion, in the absence of force, tends to continue indefinitely, rotational motion has its own way of lingering. This kind of persistence is called “conservation of angular momentum.” Recall that angular momentum is the product of an object’s mass, its rotational velocity, and its distance from the axis of rotation. One outcome of this conservation law is that if a rotating body pulls in its bulk, reducing its radius, it tends to spin faster—the total angular momentum remains constant—so if one quantity, say the distance, decreases, one of the others, say velocity, must increase. Due to conservation of angular momentum, therefore, a pirouetting skater is able to whirl at impressive speeds after drawing her arms closer to her torso. Similarly, pulsars spin considerably faster than the much larger stars from which they evolved.
The conservation of angular momentum is the reason that Earth and the other planets rotate today. The solar system, in its youth, was a whirlpool of gas and dust. As it coalesced into the Sun and the nine planets, they each retained a portion of the original whirlpool’s angular momentum—hence, each must also rotate. Similarly, in the amusement park example, if you had a sensitive frictionless gyroscope in your hand while the rotor was moving, it could continue to spin after the ride stopped.
In our search for a scale-free law uniting the cornucopia of astronomical systems, angular momentum provides an important clue. Along with mass, it is a fundamental way of classifying objects in the cosmos. Indeed some objects, such as black holes, are distinguished only by these two parameters (supplemented in certain cases by electric charge).
With the goal of a scale-free principle in mind, we can construct a simple relationship between angular momentum and mass that appears to describe many rotating astronomical systems on a variety of scales. The rule says that angular momentum is proportional to