“This planet goes this way, that rocket goes that way” – except that some – in

fact, many – objects move without moving. Or, more precisely, they move without going

anywhere.

I’m talking objects that spin, revolve, rotate, pirouette, orbit, circle, gyrate,

whirl, twirl, cartwheel, and so on. Like a planet around a star, an electron in an atom,

or even our solar system going around the gravitational center of the milky way: from

up close they’re certainly moving, but in the grand scheme of things, that motion doesn’t

take them anywhere.

We can still talk about it, though: just like “momentum” is a concept that describes

how much oomph an object has when it moves in a straight line, “angular momentum”

is a way to account for how much oomph objects have when they’re going in circles – figuratively,

or literally.

And angular momentum is simple, in theory: pick a point, any point. Pretend your object

is moving in a circle around that point. Figure out how fast the object is moving along the

circle (never mind that it probably isn’t moving exactly along the circle, and that

the circle might have to change size over time to follow the object), then multiply

that speed times the size of the circle and the object’s mass, and there you have it:

angular momentum.

For example, a 2 kilogram 60 cm-diameter bicycle wheel going 20 km per hour would have an angular

momentum of about 7 kilogram meters squared per second.

The reason we care about angular momentum is that if you take a bunch of objects that

are interacting electromagnetically or gravitationally or whatever, and add up all of their angular

momenta into one number, then that total value won’t change over time (unless some other

objects from outside come in and mess things up).

So earth, which is 150 million kilometers from the sun, orbits at 30 km/s and has a

mass of 6*10^24 kilograms, has an angular momentum of 2.7 * 10^40 kilogram meters squared

per second. That’s four thousand quintillion quintillion bicycle wheels! And this angular

momentum stays roughly constant over the course of the earth’s orbit year in and year out.

But what’s amazing is that even if the sun and the rest of the solar system were to suddenly

disappear, the earth would STILL have that same angular momentum about the point where

the sun WAS. Without the sun’s gravity, the earth would of course now move in a straight

line, requiring an ever-larger imaginary circle as it got farther from the point where the

sun used to be. But as the earth continued through space, its 30km/s velocity would also

point less and less along the circle, so when you calculated the angular momentum, the decrease

in velocity would exactly cancel out the increase in the size of the circle, and you’d always

get the same answer. 2.7 * 10^40 kilogram meters squared per second.

So even when nothing is rotating at all, angular momentum is still conserved. And that’s

the beauty of a law of physics – it works even when you try to break it!