Posts Tagged ‘Olympic’

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Winter Olympics: Why do figure skaters spin so fast?

February 15, 2018

Here is the sensational pairs team from the 2018 Winter Olympics.

But why do ice skaters spin so fast?

Here is the math!

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

Louisa Barama, USA

Louisa Barama, USA

Let’s have a look at this equation:

Figure skate maths1

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 :  vr = 308 RPM

Other spins include:

Mao Asada, Japan, triple Axel

Mao Asada, Japan, triple Axel

Triple Axel spin vr = 220 – 280 RPM

……………………………………………………………………………………………..

 Maximum Triple Axel spin vr = 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 vr = 90 RPM

More info here.

Kim Yuna, South Korea

Kim Yuna, South Korea

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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 (v1 ) from Angular Velocity (vr ). 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.

Patrick Chan, Canada, Camel Spin

Patrick Chan, Canada, Camel Spin

Patrick Chan, Canada, Triple Axel

Patrick Chan, Canada, Triple Axel

figure skate maths 2

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 vr = 90 RPM

…………………………………………………………………………………

Triple Axel spin vr = 4 x 90 RPM = 360 RPM

That’s about right.

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One Second

June 27, 2016

1 Second Logo

1 Second Logo 2a

1 second 1 Mathspig1 Seccond 2 Mathspig1 Second 3 Mathspig

1 Second 4 Mathspg

1 Second 5 Mathspig1 Second 6 Mathspig1 Second 7 Mathspig1 Second 8 Mathspig

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Lego Olympics Flags

February 23, 2012

The Lego Marching band is rehearsing for the Opening ceremony.

Lego Olympics 2016

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………….Bandito (Republic of Baddies)

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Mr Boopy (Bozonia)

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Gorilla Suit Guy (Halloweenotopia)

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………………..Barry the Butcher (Alien Steakistan)

……………..BioHaz (Toxorama)

…………………Dead-Eye Doc (AyeAwArghia)

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Dr Jabb (Bummerville)

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Hula Lula (Grinmania) 

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1. Flag Fractions

EQUIPMENT: Mixed Lego Blocks

Here is the maths. It’s fractions. It’s simple.

………………..

…………………………………………………

A. National Flag of  Comotosia

They’re a bit sleepy in Comotosia so you better design a flag to wake them up, mathspigs.

The flag must measure ………….   6 blocks x  12 blocks.

One block is a 4 bumps blocks (See pic). An 8 bumps block equals 2 blocks.

……………………

Here’s the catch, mathpiggies.  1/4 of the blocks in the flag must be RED.

How will you do this? (Hint below)

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

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.B. National Flag of Bordom

Once again the Bordonians need a lively flag.

The flag must measure 6 blocks by 12 blocks, but this time it must contain 1/4 red and 1/3 blue. How do you do this?

Hint: Mathspigs! You will have to count the number of red and blue blocks.

 

2. Design A National Flag to Lego Scale

First, name your Lego man, girl or alien and pick a name for their country, planet or crypt.

You will be drawing two flags.

All national flags are rectangles except Switzerland and Tibet, which have square flags but not at the Olympic Games.

Olympic Flags measure:  150 cm x 90 cm

or …………………………….. 60 inches x 35 inches.

These sizes are not equal so which flag is bigger the decimal flag or the Imperial Units flag?

The Imperial units flag is 152.9 cm x 88.9 cm. It turns out the area of the Decimal flag is 13,500 cm2 and the Imperial Flag 13,593 cm2

You will be designing a decimal flag.

Note the Flag ratio of length: width = 150 : 90

…………………………………………………… =  15 : 9 = 5: 3

First design a flag with 5: 3 ratio.  One measuring 10cm x 6 cm would be ideal.

 

BUT

How big are the national flags at the Lego Olympics:

Real flags at the Olympics =  150 x 90 cm

Lego Flag measurements =  150/50 x 90/50 = 3 cm x 1.8 cm = 30mm x 18 mm

Here are my two Lego people with flags  I prepared earlier:

The Enforcer from the Constellation of Obeymia and Mr Boopy from Bozonia.