Posts Tagged ‘rate’

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Winter Olympics 2022: Why do figure skaters spin so fast?

February 3, 2022

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

…………………………………………….

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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1 Year COVID-19 … some curious stats

January 22, 2021

Mathspig has tracked the Covid 19 Stats through the Worldometer tracker and calculated the AVERAGE NO. DEATHS per day at the 50607080, 100 , 200 DAY mark …

and now at the 1 YEAR mark.

 


 


 


New York Times article here.

BBC article here.

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DAY 200 Covid-19 .. some curious stats

August 8, 2020

Mathspig has been tracking the Covid 19 Stats through the Worldometer tracker and calculating the AVERAGE NO. DEATHS per day at the 50, 60, 70, 80,, 100 and now, the 200 DAY mark. The average is still rising which, as the average started low, is not good news. What can I say? Mask Up, folks. 

MATHSPIG is reporting in from lockdown in MELBOURNE, Australia, where mask-wearing outdoors is now compulsory, there is an 8pm-5am curfew and travelling more than 5km from your residence is banned.

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CONTAGION: How JUDE LAW got the PANDEMIC MATHS wrong!

August 4, 2020


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Day 100 Covid-19 .. Some Curious Stats

May 5, 2020

Day 100 of World Wide Covid-19 data.

 

Finally, the New York Times published graphs that show the severity of the Coronavirus death rate compared with average weekly death rates. Here is the graph for New York City, which shows during the peak of the Covid-19 Crisis there were 6,000 more deaths per week than expected from the average weekly death rate, which was approx. 1,000.

The death rate was 6 times the average death rate. That is a terrifying statistic and explains why we are all in lockdown or are slowly coming out of lockdown. Meanwhile, in the rest of the world death tolls are still increasing.

Excellent Covid-19 stats update here.

 

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Day 80 Covid-19 .. Some Curious Stats

April 17, 2020

Many statisticians are using 3-day and 7-day averages to track the Covid-19 death and infection rates worldwide. 

 

Mathspig is using the total average of deaths per day since stats were first published from 22 JAN 2020. When this average drops … that will be a sign for cautious optimism. But not yet!!!!

Excellent Covid-19 stats update here.

 

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DAY 70 Covid-19 .. some CURIOUS Stats

April 4, 2020

Excellent Covid-19 stats update here.

If no preventative measures were taken by governments around the world then we could have been looking at a Plague Worse Case Scenario here.

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DAY 60 Covid-19 .. some CURIOUS Stats

March 22, 2020

Excellent Covid-19 stats update here.

Worse Case Scenario here.

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Math Joke 3:How long will it take you to grow a really bad 70s-styles haircut?

February 18, 2019

1 Mathspig 1980s hair

2 Hair follicle

The follicle diagram (above) came from bgoffforensics blog. More on hair growth rates here.

QUESTION 1:

3 Mathspig how old is your hair!!!!

How long to grow that really bad 70s style hair cut?

The length of Fabio’s hair (below) is approx 50cm.

t = 50/1.25 months

t=40 months          

t = 3 Years 4 months!!!!

Is it worth the effort? Ha!

4 Mathspig 1970s celebrity hair

QUESTION 2: 5 MAthspig world's Longest Dreads

The growth rates of 1.25 cm/month or 0.5 inches/month are rounded off. Calculations using these growth rates will produce different answers for very large numbers (as above). Read more about the above story in the Daily Mail, UK here. By the way, Asha has been growing her hair for 25 years. Her hair weighs 3 stone or 19 kg. You can find more hair records including the World’s longest ear hair here.

QUESTION 3:

6 Mathspig Natasha's hair

Natasha lives in Rio de Janeiro, Brazil. Read more about Natasha in the Daily Mail here. Once again Mathspig has rounded off the length of hair for easy calculation. The Daily Mail puts Natasha’s ‘mane’ at 5 feet 2 inches or 157 cm. This is the length of hair to be cut off. So Mathspig adjusted the length to 180cm or the approx length of her longest hair.

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3. You can out run machine gun fire

January 12, 2019


Mathspig is amazed. She didn’t think there would be any hope of survival. But if the baddies sweep the machine gun tracking you as you run then …. see calcs below.

Are you feeling lucky Punk?