## 1. The Real REASON why figure skaters can spin so fast

January 23, 2014

# REASON 1:

Well, mathspiggies, the girl in this video is right. Angular momentum remains constant unless external forces are applied.

# L = mvr

L = angular momentum

v = linear velocity

r = separation of object

Let’s have a look at this equation:

The fastest spin on ice skates was achieved by Natalia Kanounnikova (Russia) with a maximum rotational velocity of 308 RPM (rotations per minute) at Rockefeller Centre Ice Rink, New York, USA on 27 March 2006. See Guinness Book of Records.

## Record spin : v_{r} = 308 RPM

Other spins include:

## Triple Axel spin v_{r} = 220 – 280 RPM

……………………………………………………………………………………………..

## Maximum Triple Axel spin v_{r} = 402 RPM

Skaters can spin faster during a triple axel jump because there is no friction from the ice slowing their spin.

To complete a quad axel, it’s estimated that the skater would have to rotate in the air at:

## 540 rpm.

…………………………………………………………………………………

## Camel spin v_{r} = 90 RPM

More info here.

## …………………………………………….

# REASON 2:

## How can a figure skater move from

## a camel spin into a very fast standing spin?

Now, mathspiggies, you must separate Linear Velocity (v_{1} ) from Angular Velocity (v_{r} ). Linear Velocity is measured in m/sec ie. it is the speed of, say, a skaters foot around the circle. Angular Velocity is measured in either RPM (Revolutions Per Minute) or degrees or Radians per minute. Ie. It is the rate of spin. We can’t judge how many m/sec a skaters foot is moving in a circle. We can only see how fast they spin. In other words, we see their Angular Velocity. When a skaters foot is in the Camel position that foot travels in a very big circle.

But when that same foot is in a Triple Axel postion it moves in a very, very small circle.

By halving the radius, firstly, a skater’s Linear Velocity doubles due to the conservation of angular momentum.

Then, secondly, by halving the radius the circumference of the circle moved by , say, the skaters foot is halved.

Overall, by doubling the velocity around the circle and halving the circumference a skater increases their rotational velocity by a factor of 4.

Look at the numbers:

## Camel spin v_{r} = 90 RPM

…………………………………………………………………………………

## Triple Axel spin v_{r} = 4 x 90 RPM = 360 RPM

That’s about right.

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by MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig …………………………………………………. with Kerry Cue | Mathspig January 23, 2014 at 6:15 amit’s the same thing in ballet. also the fast the rotation is the more stable is the balance!

by Summer Zheng January 23, 2014 at 5:27 pmVery interesting Summer. This is true. There is, of course, more friction in ballet than on ice. Cheerio Mathspig

by mathspig January 24, 2014 at 1:47 amHello. I enjoyed your article a lot and it was very informative, but I have a report in calculus where I have to see the maximum number of rotations that can be done in an axel jump and I’m really confused as to what I am looking at and how calculus applies to it. Can you explain how you got things like 540 rpm for an quad axel and how I can look at my question to answer it? I’m also thinking I would have to change my question to maximum rpm instead of rotations. I’ve done a lot of research and I’m sincerely confused right now, so if you help, it is greatly appreciated.

by Ari M January 4, 2015 at 7:55 pmThanks for your time and I hope you have a wonderful new year!

Hello Ari,

We’re on summer holiday down here in Oz. I hope you worked it out. Ciao Mathspig

by mathspig January 30, 2015 at 1:01 am