The Physics Of Figure Skating

That Outfit!

In the 1980s, nobody batted an eye at strange outfits. However, US Champion figure skater Tiffany Chin exploited fashion at the 1984 US Figure Skating championships. Chin's gaudy outfit, which involved large bracelets on both arms, did not draw excess attention, nor did the small but dense blocks of lead that she installed in her skates. Her bracelets (also made of heavy materials) and boots allowed her to show off unprecedentedly long spins with incredible speeds.

Judges suspected her physically-advantageous fashion choices when they observed her suspiciously strong forearms straining during spins. While she was not disqualified, later rule changes prohibited any jewelry in skating outfits.

Rotation Speed

Why do some spins start slowly before speeding up?

When a skater starts a spin, he would typically want it to be a bit slower compared to their top speed to that he can find his balance and center the spin. This helps the skater avoid propagating any errors from the entry into later stages of the spin, where they could cause a fall. The physics of the speed-up itself comes from the concept of moment of inertia:

Applying Rotational Motion To Rotating Skaters

Let us assume that a spinning skater is rotating about a single point on the ice (as described in the spin page, they don't, but we can ignore that here). In this case, we can describe his motion using the equation

                                                   

Since skaters cannot push off the ice to get additional energy after entering the spin, kinetic energy is conserved. If we use basic algebra, we will see that decreasing the moment of inertia will increase omega, the skater's angular velocity. Also note that there is indeed a force of friction at play causing the spin to slow. Otherwise spins would last indefinitely

Great! So How Do We Reduce I?

It's a little more complicated than a one word answer, but let's assume the skater is a cylinder:

                                                         

According to this equation, one option is to tell the skater to lose some weight. However, many skaters are very self-conscious about their figure, so this could give them some sort of complex. A better option would be to reduce the radius of the cylinder, which skaters can do by pulling in their arms and free leg. In fact, a scratch spin, which is generally the fastest spin in skating, has skaters wrap their free leg around their body to get the tightest radius possible:

                        

          Elena Sokolova Preforming A Scratch Spin, 2004

Didn't you say that I was more complicated than that?

It is, in fact. Figure skating judges are fickle people, and they are rarely satisfied with just an upright spin, even if it is blisteringly fast. Two common variations of spins include the sit spin (in which the skater does a one foot squat while spinning) and the camel spin:

   Michael Weiss Preforming A Camel Spin, 1998 Olympics

It is very clear that the camel spin is physically different than the upright spin. In this case, the skater's spinning radius is fixed at his height, and the moment of inertia is more appropriately calculated as a rod rotating about its center rather than a cylinder. All of this means that a camel spin is generally much slower than other types of spins.

Combination Spins

Taking the above information into account, it makes sense that skaters are able to do such dizzying combinations as going from a camel spin to a sit spin to an upright spin while maintaining a constant speed: by continuously decreasing their moment of inertia, they can maintain a constant spin velocity over a long period of time rather than "cashing out" for speed all at once.