Physics of Skating
Source: Smarter Everyday Day 110
Calculate Friction
Spin
When performing those rotations that figure skaters do, they use the pick at the tip of the skate to balance them by digging into the ice a little bit and skating backward on a small area called the ball of the foot.
Jumps
When jumping you use the toe pick to have a solid grip into the ice to jump up and land on the toe pick to spike the ice so that you don't slip and then plant the rest of the blade and then use the momentum from the jump to move.
Hockey Skating
The blade actually has 2 edges on it and depending on how quickly you want to be able to stop you decided the radius of the blade. The greater the radius the more grip you have thanks to being able to cut into the ice.
Then a hockey player wants to stop you control the edge of the blade to scratch the top layer of the ice off to reduce speed. Based on how fast you want to stop and how fast you are stopping right now you change the angle of the skate to decide how much ice you want to scrape to convert that sheer force to stopping power.
Speed Skating
The bottom of a speed skate is actually a flat 90-degree angle since you want more contact to decrease the bite.
This makes it harder to create a force so they rotate their foot to get an angle on the size to use the edge to push off.
