At one level, skating is skating is skating.
Whether it is hockey, ringette, speed skating or figure skating, the underlying physics involved in moving across an ice surface is the same. Indeed, the basic physics behind skating is just Newton's Laws of Motion.
Newton's First Law tells us an object at rest will stay at rest but an object in motion will stay in motion - unless a force is applied. In the case of skating, once a skater has built up speed, they can glide for a long distance. The slipperiness of ice reduces friction allowing a skater to remain in motion without additional effort.
This is perhaps best seen in figure skating where athletes will coast for long periods setting up for a particularly difficult jump.
Newton's Second Law tells us acceleration is the result of the application of force to a mass. The greater the force applied to a given mass, the greater the acceleration.
Hockey players switching direction and power skating to full speed rely on this. In long track speed skating, maximum force is applied at the beginning of a race as the athletes are sprinting across the ice.
In figure skating, the second law controls the graceful curves. A change in velocity, which is both speed and direction, requires acceleration. Travelling in a circle, for example, at a constant speed involves acceleration because of the constantly changing direction.
Newton's Second Law also explains why female figure skaters who are much smaller than male skaters can still go as fast. Less mass means less force is required for the same amount of acceleration. Indeed, less mass has all sorts of advantages in figure skating.
Newton's Third Law says that for every action, there is an equal and opposite reaction. This is basis of all forms of skating. As the blade digs into the ice, the skater pushes against the edge applying force backwards. The result is forward motion in a direction opposite to the push.
However, while Newton's Laws underlay all forms of skating, there is even more physics involved. For example, figure skating is also about combining projectile motion and angular momentum to maximum effect.
Projectile motion is the motion a ball might take if thrown over a short distance. It is a parabola where the take-off and landing angles are the same. It is combination of vertical and horizontal velocity with the acceleration due to gravity.
As a skater leaps into the air, they have maximized their vertical velocity but gravity slows them down. At the top of their jump, their vertical velocity is exactly equal to zero and they start to descend. Gravity takes over and they are brought back to earth.
The amount of time in the air is dependent upon the take-off angle and velocity. For a skater moving at 10 m/s or 36 km/h (a typical speed for a figure skater), if they leap into the air at a 45 degree angle, their vertical velocity will be 7.1 m/s. This will translate to a hang time of 0.723 seconds and a height of slightly over two metres for the jump.
If they are trying to do a triple toe, they have exactly that long to complete three rotations. (In a triple Axel, they actually have to complete 3.5 rotations in that time.)
This is where angular momentum comes into play. In order to complete three rotations in 0.723 seconds, figure skaters must spin at 240 rpm. That is at the low end of what you might find in an internal combustion engine, but still pretty fast.
To achieve this rate of spin, a skater uses their time coasting across the ice to prepare their arms. By spreading their arms wide and then pulling them in at the same time as twisting their body on take-off, they are able to conserve their angular momentum.
The result is a rapid spin.
The effect arm position has on a skater's rate of spin is perhaps better seen during the spin component of the program. Bringing their arms from an extended position to close to their body dramatically increases the rate of spin. Changes in the rate of spin are also seen when an athlete changes position such as going from a camel spin to a sit spin.
It is the combination of arms and legs working in unison, though, that allow figure skaters to pull off triple and quadruple jumps. Of course, the various jumps also rely upon using the toe pick correctly and on having soft ice. Then there is the 4g of force that they have to fight just to bring their arms into position and the 7g of force they experience on landing. Yes, there is lots of science.
Figure skating is skating, but in many ways it is a most demanding sport.