## Saturday, December 9, 2017

### The Physics of Figure Skating

When watching figure skating on TV this past week, I was amazed at how the men were able to perform fully rotated quadruple jumps. Quadruple jumps are mostly only done my male figure skaters, as it requires a lot of strength and force to be able to jump high enough to complete four full rotations in the air before landing. Besides jumping high, these men need to have a very great rotational speed in order to complete the rotations in the very short amount of time in the air. When watching Nathan Chen, the only male figure skater who has completed five quadruple jumps in a program, I saw that his average time in the air is 0.7 seconds. By using the equations:

θ =  ω0t + ½ αt 2

ω2 = ω02 + 2α(θ − θ0)

I was able to predict how fast he had to rotate in order to complete these rotations. When skaters do a jump they have to jump up straight before they start rotating, which means their initial rotational speed is 0revs/s. Using a rotational distance of 4 revolutions and a time of 0.7 seconds, I got an angular acceleration of 16revs/s, which then, using the second equation, gives you a final rotational speed of 11.3revs/s. This is a very fast rotational speed, and it requires a very small moment of inertia, which these skaters produce by keeping their arms and legs in very tightly. If you want to see this in action, attached is a video of Nathan Chen’s quadruple jumps.