Archive for the ‘units speed’ Category

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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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The Lego Olympics 2020

July 30, 2021

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Toilet Paper FUN FACTS Maths

June 1, 2021

Mathspig is in Melbourne, Australia. We’re in Lockdown. AGAIN!

And toilet paper has disappeared off the supermarket shelves. AGAIN.

So today we are doing maths based entirely on toilet paper using information from the Toilet Paper Fun Facts website. Yes! It exists here.

Toilet Paper Fun Facts Website

Protractor Wind Speed Calculator

POP UP ANS Q 1 & 2 Yr 7&8 Toilet Paper fun facts

Traxxas XO-1 Website

Pythagoras Equation Diagram here

Here is the Sine Rule (Watch 1.5 mins)

Check sine curve here:

Listen to sine curve here:

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Ohtani vs The World ………………………. Some amazing fastball facts.

April 12, 2021

More Info: New York Times, 5 April 2021

Also: Which sport is more DANGEROUS to play? Cricket or baseball?

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Tennis Math: Is player height a BIG advantage? USA units

February 13, 2021

Metric version here.

The Australian Open is on at the moment in Melbourne in LOCKDOWN. (We have 1 community-acquired case. Tennis players are in a bubble.)

Is height a BIG advantage in tennis?

Here are the heights of 3 top seeds in the Australian  Open. (See graph below)

No. 1 Novak Djokovic    6ft 1″  (73 in)

No. 6 Alexander Zverev  6ft 6’   (78 in)

No. 8 Diego Schwartzman  5ft 7’  (67 in)

1. Does serve speed increase with height?

That would be an advantage. Here is a Height vs Serve Speed chart for the Top 6 seeds in the tournament:

Find serve speed data here.

There is NO CLEAR HEIGHT ADVANTAGE for serve speed.

2. Does the serve return rate increase with height?

Here is Diego Schwartzman (L) when he defeated Alexander Zverev (R ) in the 2019 US Open.

What is Schwartzman’s Super Power?

Schwartzman, the shortest player on the circuit (see graph above), tops the service returns stats. Highest 2nd serve return rate. Third highest 1st serve return rate. See data below. So agility, speed, and reaction times are also important factors in becoming a tennis star.

Go Schwartzee! Check data here.

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Tennis Maths: Is player height a BIG advantage? Metric

February 13, 2021

USA units post here.

The Australian Open is on at the moment in Melbourne in LOCKDOWN. (We have 1 community-acquired case. Tennis players are in a bubble.)

Is height a BIG advantage in tennis?

Here are the heights of 3 top seeds in the Australian  Open. (See graph below)

No. 1 Novak Djokovic  188cm

No. 6 Alexander Zverev  198cm

No. 8 Diego Schwartzman  170cm

1. Does serve speed increase with height?

That would be an advantage. Here is a Height vs Serve Speed chart for the Top 6 seeds in the tournament:

Find serve speed data here.

There is NO CLEAR HEIGHT ADVANTAGE for serve speed.

2. Does the serve return rate increase with height?

Here is Diego Schwartzman (L) when he defeated Alexander Zverev (R ) in the 2019 US Open.

What is Schwartzman’s Super Power?

Schwartzman, the shortest player on the circuit (see graph above), tops the service returns stats. Highest 2nd serve return rate. Third highest 1st serve return rate. See data below. So agility, speed, and reaction times are also important factors in becoming a tennis star.

Go Schwartzee! Check data here.

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Terrifying Tennis Maths: The Speed of Novak Djokovic’s serve. METRIC

February 7, 2021

USA units post here.

Novak Djokovic is the No. 1 Seed in the Australian Open 2021.

His fastest serve = 219 kph

Could you return his serve? Do the maths!!!!!!

The ball leaves Djokovic’s racket and hits the ground 0.31 secs later.

Go here to see why this simplified calculation works! 

Mathspig tested her reaction time here. TRY IT!

Mathspig’s best, best, best reaction time = O.33 sec

The fastest serve EVER was delivered by Australian Sam Groth @ 263 kph.

That serve takes 0.25 sec to land on the other side of the court.

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Terrifying Tennis Math: The Speed of Novak Djokovic’s serve. USA units

February 7, 2021

METRIC post here.

Novak Djokovic is the No. 1 Seed in the Australian Open 2021.

His fastest serve = 136 mph

Could you return his serve? Do the math!!!!!!

The ball leaves Djokovic’s racket and hits the ground 0.30 secs later.

Go here to see why this simplified calculation works! 

Mathspig tested her reaction time here. TRY IT!

Mathspig’s best, best, best reaction time = O.33 sec

The fastest serve EVER was delivered by Australian Sam Groth @163.4 mph. That serve takes 0.25 sec to land on the other side of the court.

 

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Real World Maths: RATES, pop song drumbeats and jogging

September 17, 2020

Jog FM Here are songs with bpm = 100

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Australian Open 2020: Could YOU ….. return Roger Federer’s serve?

January 27, 2020

The Australian Tennis Open is being played at the moment and Mathspig is always amazed at the serve speed of the top-seeded players.

Here are some of the serves speeds of players in this year’s Men’s Open. 

Keep in mind the fastest female tennis serve by Barbora Záhlavová-Strýcová is a very respectable 225 km/h (140 mph).

Can you return Roger Federer’s serve?

NOTE: Andy Murray had the same serve speed as Roger Federer.

Go here to see why this simplified calculation works! 

Mathspig tested her reaction time here. TRY IT!

Mathspig’s best, best, best reaction time = O.33 sec

Could Mathspig return Roger Federer’s serve?

Nooooo!…………………………………………………………………….

I’d be hit in the head by a speeding tennis ball

before I even moved.

But I’m a pig. I’ve got the best service GRUNT! Ha!