Does Angular Momentum Make Your Head Spin?

I was recently asked about things that spin in the universe. Planets spin. Stars spin. Galaxies spin. Why do they spin, and how do they acquire that spin?

This blog post contains my response. I’m going to go through things slowly, and build up concepts, so bear with me.

A spinning top [Credit: randomname123 at tenor.com]

The main concept for understanding spin in the universe is “angular momentum” as a conserved quantity.

In physics, conservation laws are of fundamental importance; including conservation of energy, conservation of linear momentum, and conservation of angular momentum. These conservation laws state that, in any closed environment, the total amount of these quantities never changes.

For energy, it can change form from kinetic energy to thermal energy. When you rub your hands together, the kinetic energy of the rubbing motion is converted by friction to thermal energy of heating your hands. The form of the energy may change, but energy in its various forms is conserved.

For linear momentum, think of a billiard ball hitting a bowling ball. The large mass bowling ball is barely disturbed, while the small mass billiard ball ricochets away at considerable speed. Linear momentum is mass times velocity. If both balls get the same momentum from the collision, the high mass object has a low velocity, and the low mass object has a high velocity.

Finally, there’s angular momentum, which is a measure of spin. For a circular motion, angular momentum is mass times velocity times the distance to the center of the circle. Earth has a roughly circular orbit around the Sun. Hence, if Earth were moved farther from the Sun, it would orbit at a slower speed to conserve angular momentum.

Cartoon diagram of the solar system (not to scale in any way) [Credit: madewithc0de]

As one can observe, the solar system does not have a net zero angular momentum. The orbits of the planets are mostly aligned in a plane, giving a net positive angular momentum. However, if the universe started out with a net zero angular momentum, how do pieces of it develop a net positive?

Since conservation requires a closed system, we must first note that the solar system does not exist in isolation, and cannot be considered a closed system. In addition, angular momentum is a vector quantity that points in a particular direction. Our solar system has net angular momentum that points roughly perpendicular to the orbital plane of the planets. Other solar systems have net angular momentum pointing in other directions. With random directions, the sum of these would generally cancel out to roughly zero net angular momentum.

The formation of stars (and thereby solar systems) takes place in a nebula. Suppose the nebula has no overall net angular momentum. As regions of a nebula collapse to form stars, they will interact via gravity and gravitational torques to allow net spin within each region, but which balance out to conserve the net zero spin of the overall nebula.

That picture is an oversimplification, as nebulae will have gravitational torques from other nebulae, with the process looking similar on larger scales. Gravity operates the same on all scales.

Spiral galaxy NGC 4414 [Credit: The Hubble Heritage Team (AURA/STScI/NASA)]

Note that galaxies, too, have net spin. That means that the sum of galaxy spins must cancel out to zero if the universe was established with no net angular momentum. It is all the same argument, just applied on a larger scale.

Now, it is not guaranteed that the universe has zero net angular momentum, and it is quite difficult to measure. It is a reasonable assumption, as there is no obvious process for generating angular momentum. But neither is there an obvious process for generating the net positive energy of the universe (i.e., what “caused” the big bang?).

Dorothy Hamill executes an amazing spin during a performance.

The other important aspect of angular momentum is often thought of as the ice skater phenomenon. When an ice skater starts a spin with their arms and legs extended, they are spinning slowly. Their angular momentum has a large distance from the center and a small speed. When they pull their arms and legs in, that reverses. A small distance from the center means a fast speed of the spin. Conservation of angular momentum at work.

Hence, a cloud that will form the solar system needs only a tiny, tiny bit of spin on large scales in order to produce rapidly spinning objects after it collapses. These nebulae start out about a hundred thousand times larger than the eventual collapsed system. That’s about a hundred thousand times increase in the velocity.

Spin is the natural result of angular momentum conservation during gravitational collapse. It happens for planets, stars, solar systems, and galaxies. Different pockets of the universe may develop different spins, but the net sum of all these spins is conserved.

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