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Physics LibreTexts

9.4 Angular Momentum in a Collapsing Cloud

Step outside and think about the air around you: it's never perfectly still. Air has two types of motions. One is the microscopic motion of the individual molecules — every molecule has a random velocity that depends on the temperature of the gas. The other motion is macroscopic, or large-scale. The Sun's energy causes the air to move in large circulating patterns. These rotating patterns can occur in any direction, and on any scale — from a little dust devil in your backyard to a hurricane hundreds of miles across! You can understand this better if you do a simple experiment using a cup of coffee. Stir the liquid vigorously, but as randomly as you can. Then wait a moment, and put a drop of cream in it. Notice that the cream rotates smoothly in one direction. This phenomenon occurs because the sum of all the random motions is a small overall rotation in one direction or the other. This effect you see in your coffee cup, and in the wind patterns of Earth's atmosphere can also be seen at the largest scales in the universe.

 


Putting a drop of cream in your sturred coffee can cause a patter like this. Click here for original source URL.


A diffuse gas cloud in space has the same two types of motion. The gas atoms or molecules have random velocities corresponding to their temperature, but the cloud also has a small amount of overall rotation. The concept of angular momentum predicts what happens to the rotation as the cloud collapses.


An earth-bound example of angular momentum in a cloud. Click here for original source URL.

Angular momentum is the quantity that measures the total rotary motion of a system. It is related to the amount of material rotating, the rate of rotation, and how spread out the rotating material may be. Mathematically, angular momentum is the product of the mass, the rotation rate, and the radial size of an object or system, L = r × m v.

A powerful principle of physics, called the law of conservation of angular momentum, states that the total amount of angular momentum remains constant as a system changes. This means that if an object shrinks, its rotation rate must increase to compensate. You're probably familiar with the example of figure skaters that spin faster when they pull in their arms.

This same effect is seen in space, although it is a bit more complex. As a star forming cloud begins to contract, the rotation rate must increase, because angular momentum is conserved. In general, a big, slowly rotating system will turn into a small, rapidly rotating system. The collapse amplifies the rotation rate. But in a rotating cloud, the gas does not collapse equally in all directions. Gas can easily collapse along the rotation axis or perpendicular to the plane of rotation. However, along the equator of the rotating cloud, the gas meets a resistance due to the rotation. This same resistance presses you against a car door when you go around a tight curve, or keeps the tension in a string when you whirl an object over your head. Thus, the cloud collapses more along the poles of its rotation than along its equator, and the effect is to squash it into a disk shape.

The theory of how the planets formed from this disk accounts for many features of the Solar System. But there is a fly in the ointment: the Sun carries over 99% of the mass of the solar system, but less than 1% of the angular momentum. The Sun does not spin as fast as it should, given the orbital speed of the planets. Why is this a problem? As the pre-solar nebula collapsed, slowly moving material far from the center sped up as it got closer to the center. So material at the center, which formed the Sun, should have been spinning rapidly. Either the planets somehow acquired "extra" angular momentum, or the Sun somehow "lost" angular momentum. Scientists currently favor the theory that that the magnetic field of the Sun interacted with fast-moving particles to "brake" the Sun's rotation speed.