Archive for the ‘units speed’ Category

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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

…………………………………………….

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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Winter Olympics: Beaten by 0.001 seconds

February 14, 2018

 

In 2014 Winter Olympics Annette Gerristen (below) lost the Gold Medal in the 1000 m Women’s speed skate competition by 0.02 seconds.

Annette Gerritsen fromthe Netherlands

Annette Gerritsen fromthe Netherlands

What are the speed skating times for women?

Women’s Speed Skating Calulations:

Here are the speed calcs for Yara Van Kerkhof of the Netherlands in the 2018 Winter Olympics:

If Yara lost the Gold Medal by 0.02 secs (2 hundredths of a second) what would the distance be between the Gold and Silver place getters?

When 1st and 2nd place are separated by 0.02 seconds, they are travelling at almost the same speed. So the second place contestant is:

23.8 cm behind the Gold Medalist

The 2018 Olympic Gold Medalist in the 500m Women’s Speed Skating was Arianna Fontana.

Italy’s Arianna Fontana wins the 500 m Speed Skating 2018 Olympic Gold Medal in 42.569 seconds ahead of Yara van Kerkhof of the Netherlands and Kim Boutin of Canada. 

Men’s Speed Skating:

At longer distances the men’s speed skating speed is similar to the women’s speed above.

If you lose by  0.001 secs…………

Apollo Ono (below) competed in the 1500m men’s speed skating. He has won 8 Olympic Medals.

If a speed skater lost the Gold Medal by 0.001 seconds, the smallest measured time segment at the Olympics, they would be:

1.19 cm

behind the winner. That is less than the length of a small fingernail.

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Hello 2018 This is why you need maths!

December 30, 2017

Hello Little Munchins,

,…………………………………………..…………………………….

Maths can save your life. How? Read on.

,…………………………………………..…………………………….

Sadly, a car has been used as a weapon again in my city, Melbourne. 

,…………………………………………..…………………………….

When talking to science types about the Maths of a Car Used as a Weapon they say ‘Yeah! Right! As if you are going to stand around doing the maths when a car is heading towards you!!!!.’……………………

NO!…………………………………………..……..

You don’t do the maths in a crisis. You do it before hand. And it will change your view of car safety for all time.

METRIC:

Maths of a Car Used as a Weapon 

If you are 9 m away from a car travelling at 60 kph, you DO NOT have time to move out of the way. 

Some survival tips at the above link.

USA UNITS:

Maths of a Car Used as a Weapon

If you are  28  ft away from a car travelling at 35 mph you do not have time to move out of the way.

Some survival tips at the above link.

Stay safe in 2018.

Cheers

Mathspig

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The Terrifying Maths of Running from a Bear … Metric Units

July 17, 2017

METRIC UNITS below. USA UNITS here.

BEAR STATISTICS

Grizzly Bear

Weight:   250kg

Height:   250cm

Top Speed: 56kph  =   16 m/sec

More bear stats here. 

Brown Bear

Weight:  680kg

Height:   250cm

Top Speed: 35kph  = 10m/s

More bear stats here.

Comparing these speeds to the fastest man on earth, Usain Bolt:

Usain Bolt:

Top speed: 243kph =   12m/s

So Usain Bolt could out run a Brown Bear but NOT a Grizzly!

Bears are NOT as dangerous as:

In fact more Americans die choking on their own vomit each year than a re killed by bears.

More death stats here.

But bears are very fast so Park Rangers recommend the following survival tactics:

More bear survival info here.

REF: Dog helps save hikers after grizzly chases them for 20 minutes here.

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The Terrifying Math of Running from a Bear … USA Units

July 17, 2017

USA UNITS below. METRIC UNITS here.

BEAR STATISTICS

Grizzly Bear

Weight:  550 lb        

Height:  8’ 2”   

Top Speed: 35 mph  =   51 ft/s    

Brown Bear

Weight:  1,500 lb       

Height:  8’ 2”              

Top Speed: 22 mph  =  32 ft/s     

Comparing these speeds to the fastest man on earth, Usain Bolt:

Usain Bolt:

Top speed: 27 mph  =   40 ft/s     

Bears are not dangerous:

………………………………………………………………………


In fact, more Americans die each year from choking on their own vomit than are killed by bears.

More death stats here

Nevertheless, bears are very fast. So you can see why Park Rangers offer the following advice:

More information at Mountain Nature.

The reason for waiting until the bear is 15 ft away is to make sure the spray doesn’t disperse in the air. If the Pepper Spray is too spread out it will not stop the bear.

Ref: Dog helps save hikers after grizzly chases them for 20 minutes.

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The Simple Maths of a Car used as a Weapon … METRIC units

February 3, 2017
NIce Truck Attack 2016 The Independent, UK

Nice Truck Attack 2016 The Independent, UK

Berlin Christmas Maraket Attack 2016, ABC

Berlin Christmas Maraket Attack 2016, ABC

Melbourne Car Attack 2017

Melbourne Car Attack 2017.

Cars (and trucks) have been used as weapons by drivers purposefully driving into crowds including:

2014: Saint-Jean-sur-Richelieu, Quebec

2014 : Jerusalem, Israel.

2016: Nice, France

2016: Berlin, Germany

2017: Jerusalem, Israel

2017: Melbourne, Australia.

What does the maths tell us?

Melbourne is Mathspig’s home town. The car attack killed, tragically, 6 people and injured many more. The question many seem to ask is:

Why can’t people get out of the way?

Look at the video below of the Melbourne car. It doesn’t appear to be going that fast. But the maths tells a different story. You need quite a distance between you and a car travelling at approx 60 kph to have enough time to run clear. (See calculations below)

How fast do you react?

We will set your reaction time at 0.4 sec. This allows time for you to react and turn. If you want to test your reaction time go here. But remember you have to turn as well.

How fast would you run?

According to the Telegraph, UK, the average human can run at 15.9 mph (25.6 kph) and the National Council of Strength and Fitness 15 mph (24.1kph), which Mathspig has rounded off to 25 kph.

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car-used-as-weapon-2
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How do you escape a car travelling at 60 kph towards you when you are less than 9 m away?

Jump upwards!

You might reduce the impact and even go over the roof.

car-used-as-weapon-4

car-used-as-weapon-5
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Smoke Jumpers and their Amazing Wildfire Maths . . . . . . . . . . . . . . METRIC UNITS

December 5, 2016

mathspig-smoke-jumpers 

With wildfires in Texas and now Australia is facing the fire season, it is time to think about fire fighter maths.

mathspig-metric-units-fire-math

METRIC UNITS

Background Story

On 5th August 1949 Wag Dodge was dropped by parachute with 14 other fire fighters into Mann Gulch, a steep-sided gully in a Montana pine forest. Fire fighters who parachute in to put out small blazes started by lightening are called Smoke Jumpers. As they worked their way down the sides of the gully the breeze was blowing away from them. But the wind soon shifted. This produced an updraft, which increases the speed of the fire front. The 15 Smoke Jumpers turned and started running for their lives uphill.

HOW FAST CAN YOU RUN?

METRIC UNITS

Time Trial:

Mark out a 10 m course. Make 3 time trials.

t1 =

t2 =

t3=

Average your time:

tav = (t1 + t2 + t3)/ 3 =

Your Speed S = 10/tav = ……… m/sec

mathspig-firefirghter-maths-1

HOW FAST IS A GRASS FIRE?

This will, of course, vary depending on the wind speed. A typical grass fire in Australia in a flat area can travel at 20kph (up to 30 kph) in a gentle breeze.

Fire Front Speed Grass Fire

Fire Front Speed = 20 kph = 20 x1000/(60 x 60)

                               = 20 x 0.27777777 = 20 x 0.28 m/sec

                               = 5.6 m/sec

mathspig-firefighter-maths-2

CAN YOU OUT RUN A FIRE?

Average Running Speed Boy 13–14 yo = 3.0 m/sec

Average Running Speed Girl 13–14 yo = 2.4 m/sec

We’ll assume, boy or girl, that you are really motivated and can run away from the fire at top speed of 3.0 m/sec. Now calculate the distance you can run and the fire front moves in 10 secs intervals up to 1 minute.

mathspig-fire-fighter-table-1

This is not looking good. See more Firefighters Need Maths here.

We can do very accurate calculations using simultaneous equations. Wildfire Algebra: Detailed Worksheet using simultaneous equations and solutions  here.

NOW YOU ARE RUNNING UP HILL. WHAT HAPPENS?

We’ll assume, due to being motivated by having a fire licking your heels, that you can run at your top speed up hill for a short time, at least. But here is the problem.

Heat rises and so there is a Chimney Effect pushing the fire uphill. The rule of thumb used by fire fighters is:

Each 10º increase in slope, the fire front speed doubles.

mathspig-cfa-diag

mathspig-fire-fighter-table-2

Now you can calculate the distance travelled by the fire front up a slope at a 30º angle.

Don’t forget you can use the WEB 2.0 Calculator here.

mathspig-fire-fighter-table-3

Even at your top running speed, which is unlikely up a slope, you can run 180 m in 1 minute. In that time the forefront has moved 2688 m or 2.7 km.

It depends how far away you are from the fire front, but it seems you cannot out run this fire front.

Again we can do very accurate calculations using simultaneous equations.

See Firefighters Need Maths here.

Wildfire Algebra: Worksheet and solutions here.

CAN YOU OUT RUN A WILD FIRE?

High winds can turn a bush or forrest fire into a WILD FIRE with wind speeds up to 110 kph and temperatures up to 2000 °C, which can and does melt glass and cars.

The fire front speed doubles with every 10º, so speeds for the fire front can reach 220 kph, 330kph and up to 550kph.

20o-angle-mathspig-2

What happened to the Smoke Jumpers?

When the fire front changed direction Wag Dodge and 14 other Smoke Jumpers found themselves running for their lives up a steep slope. What did Wag do next?

ANS: Here’s the amazing thing. Wag realised he could not out run the fire at that point. So he stopped. Took off his back pack. Took out some MATCHES and lit a fire in the grassy patch in front of him. Just before the firewall hit he threw himself face down on the burnt patch. He survived. The other 14 firefighters did not.