What Does This Ice Skater Have In Common With A Neutron Star?
Classical Mechanics
Level
1
Which fundamental physical principle is crucial to the behavior of both the skater and the pulsar?
Conservation of linear momentum
Precession
Conservation of angular momentum
Electromagnetic radiation
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11 solutions
The image on the left is of a spinning ice skater. If you’ve ever watched ice skating you’ll notice that ice skaters often finish their routine with a spin. They start out with legs extended, spinning slowly, then bring their arms and legs in and begin to spin incredibly fast. Ice skaters speed up due to conservation of angular momentum. Angular momentum is the tendency of a rotating object to keep rotating, and the total angular momentum of an object is conserved, or unchanging, if the object is isolated (as a skater is - the ice doesn’t provide much friction). Now, the skater starts rotating with her arms and legs extended and if you thought about stopping her rotation you’d realize it’s quite hard to stop someone rotating if they have their legs straight out (it’ll hurt as you’re kicked in the belly). In other words, she has a lot of angular momentum. As she brings her arms and legs in, she changes her shape to a configuration that is intrinsically easier to rotate. Since her angular momentum is conserved, she therefore begins to rotate faster, so that it is just as hard to stop her with her arms and legs in as it is with her arms and legs out.
The image on the right is an x-ray image of a pulsar. To understand pulsars, we first need to understand what happens when stars run out of fuel. When stars run out of fuel they collapse under their own gravity and form different kinds of objects. Smaller stars will form white dwarfs, while the biggest stars will form black holes. Intermediate sized stars can, however, form what are called neutron stars. A neutron star is a very dense ball, roughly 10 km in radius, made up of neutrons. The density is so high that a few cubic centimeters of neutron star has a mass of a trillion kilograms. A pulsar is a rapidly spinning neutron star. Some pulsars even spin at over 100 full revolutions a second! (Just try to picture that in your mind for a second: a sphere of radius 10 km, with a huge total mass, spinning at 100 revolutions per second.)
Pulsars spin so fast due to conservation of angular momentum, just like the ice skater. Consider a star collapsing to a neutron star. In general stars rotate, and when they collapse their total angular momentum can’t change. Just like the ice skater bringing her arms in, the star starts rotating faster. Since the radius of the sun compared to a neutron star is huge, they speed up a lot. The resulting pulsar has a rapid angular speed and a tremendous amount of rotational kinetic energy. The rapid spinning generates strong magnetic fields and heats up any gas surrounding the pulsar, which then emits electromagnetic radiation preferentially along the axis of rotation as you can see in the image above. Pulsars originally got their name from this behavior: we see intense pulses of radiation from the pulsar as its preferred axis sweeps past the line connecting the pulsar with earth. Since there is so much angular momentum in the pulsar they tend to remain unchanged, similar to how a rapidly spinning top stays unchanged for a long time. Hence the pulsing of a pulsar is one of the most accurate natural clocks in the universe.
The moral of this story is that the same physical laws you see everyday are often responsible for the most exotic phenomena. Hopefully this will shed new light on things as you watch the skaters in the next winter Olympics.