## Archive for the ‘algebra’ Category

## No Frills MATHs SKILLS for Parents 3: Pre-Algebra

May 23, 2022## No Frills MATHs SKILLS for Parents 2 : Algebra

May 4, 2022## 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

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.

## WINTER OLYMPICS: How ski Jumpers Use Math to Increase their Jump Length

February 3, 2022**While air resistance has little impact on aerial skiers it is a significant factor used by ski jumpers to increase their jump distance.**

**The significant maths for ski jumpers is therefore X-section area.**

**Here is the jump at Pyeong Chang, 2018. Just imagine going down that at top speed!!!**

**Ski jumpers increase their speed going down the ramp by reducing their X-section area:**

**Once they leave the ramp, ski jumpers try to increase their X-section area like Ski Divers to slow their vertical fall. But they have to land safely so they keep their skis at a minimum angle.**

# Here are the X-section areas for Abby Hughes*:

**Here is the formula for Air Resistance of Drag:**

*D *= ½*CApv ^{2}*

**Where C is the drag coefficient or constant, which depends on the shape and spin of an object. It is found by testing the object in a wind tunnel.**

*A* is the X-section Area,

*p* is the density of the air and

*v* the velocity of the object.

**More here.**

**As Abby Hughes has tripled her X-section area in the air, she will ****have tripled the vertical drag during her jump. This will slow here decent.**

*Mathspig calculated the X-section area by the old fashioned method of counting squares and rounding off the final count. Mathspig sized the two pics of Abby Huges so that her head was the same size in both pictures.

## WINTER OLYMPICS 2022: One Rule Aerial Skiers Cannot Break

February 1, 2022# The Parabola Must Be Obeyed!!!!

Aerial skiers aim for height rather than length. Their aerial flight times are much smaller than ski jumpers so air resistance has minimal impact.

In fact, there is one law the aerial skiers cannot break. It is the law of gravity.

Here is an equation for projectile motion from Wired magazine.

The equation for projectile motion also applies to **Motorbike Jumps** and **Longbow Arrows**.

Here is the x-y graph for different launch angles.

You can go to this page for complete calculations. Aerial skiers twist and turn but their CENTRE OF GRAVITY must follow this graph. More on centre of Gravity at The Great Back Pack Attack ie.

The centre of gravity of Aerial Skiers must follow a

# parabolic curve.

## Death by Caffeine: The Maths Part 1 METRIC

November 26, 2021Death by Caffeine: The Math Part 1 USA UNITS **here**.

The lethal dose for **caffeine** is about 150 milligrams per kg of body weight. While the average person’s **caffeine** consumption is around 200 milligrams a day, the Mayo Clinic advises against exceeding 500 to 600 milligrams per day.

This work titled Timing is Everything is by street artist ABOVE in London.

You may want this much energy but be warned, energy drinks can kill.

It would take a ridiculously huge number of ANGRY WOMBAT energy drinks to kill a 14 year old weighing, say, 48 kg. Nevertheless, some kids are more sensitive to caffeine than others and then much lower levels of consumption of energy drinks can be fatal.

See Death by Caffeine: The Maths Part 2 METRIC

Here is the work (see below) TIMING IS EVERYTHING by street artist ABOVE in London showing the timing.

## Death by Caffeine: The Math Part 1 USA UNITS

November 26, 2021Death by Caffeine: The Maths Part 1 METRIC **here**

The lethal dose for **caffeine** is about 68 milligrams per lb of body weight. Average consumption of caffeine is about 200 milligrams a day. The Mayo Clinic advises against exceeding 500 to 600 milligrams per day.

This work titled Timing is Everything is by street artist ABOVE in London.

You may want this much energy but be warned, energy drinks can kill.

It would take a ridiculously huge number of ANGRY WOMBAT energy drinks to kill a 14 year old weighing, say, 110 lb. Nevertheless, some kids are more sensitive to caffeine than others and then much lower levels of consumption of energy drinks can be fatal.

See Death by Caffeine: The Math Part 2 USA UNITS

Here is the work (see below) TIMING IS EVERYTHING by street artist ABOVE in London showing the timing.

## Maths in the Real World: 10 Attention Grabbers for Middle School

September 5, 2021## 1. Smoke Jumpers: The Amazing Maths of wildfires

## 2. The Rolling Coin Paradox!!

## ROLLING COIN PARADOX HERE

## 3. How barcodes work!

## Barcode MATHS HERE

## 4. Pop Song Beats and Jogging

## 5. Linear Math and Linear Drumming. It’s a thing!

## 6. Powers and the Loudest Rock Band in the World

## Powers and the Loudest Rock Band MATHS HERE

## 7. Alcohol Kills! Calculate how much would kill you!

## Alcohol Kills! MATHS HERE

## 8. Tall Tales: Is height the most important factor in sport?

## Height in Sport maths: METRIC UNITS HERE

## 9. Mmmmm! Chocolate. Yes! It can kill you

## 10. Random Music? You think!

## Random Music?MATHS HERE

## Toilet Paper FUN FACTS Maths

June 1, 2021Mathspig 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**

**Pythagoras Equation Diagram here**

**Here is the Sine Rule (Watch 1.5 mins)**

**Check sine curve here:**

**Listen to sine curve here:**

## 20 Gobsmacklingly AMAZING numbers … Revisited

May 25, 2021## … these nos. are amaaaazing but no one could find the answers in the earlier post.

## ………………………………………………………..

## Click on the POP-UP answers under each question.

**1. How many bristles in a toothbrush?**

**2. What % of Oxygen in the atmosphere comes from forests?**

**3. How loud was the loudest recorded human scream?**

**4. How many apples could kill an average-sized adult?**

**5. How many countries in Africa?**

**6. What happens when you Google this number, 241543903?**

**7. How many vertebrae in a giraffe’s neck?**

**8. What is the highest recorded wind speed?**

**9. What is the world record high-jump height for a guinea pig?**

**10. How many times does England fit into Australia?**

**11. How much did the most expensive dessert ever cost?**

**14. How many burgers does McDonalds sell a second worldwide?**

**16. How many times was the most frequently married person in the world, married?**

**17. Why is Zero Zero Zero like 123?**

**18. What is the world record for the greatest number of snorts in 10 seconds?**

**19. How long would it take to grow your hair to your feet?**

**20. What number causes the greatest loss of money in the world?**

## LINKS:

1. How many bristles in a toothbrush? **HERE**

2. What % of Oxygen in the atmosphere comes from forests? **HERE**

3. 3. How loud was the loudest recorded human scream? GOOGLE IT!

4. How many apples could kill an average-sized adult? **HERE**

5. 5. How many countries in Africa? GOOGLE IT!

6. What happens when you Google this number: 241543903? **HERE**

7. How many vertebrae in a giraffe’s neck? **HERE**

8. What is the highest recorded wind speed? **HERE** and **HERE**

9. What is the world record high-jump height for a guinea pig? GOOGLE IT!

10. How many times does England fit into Australia? GOOGLE IT!

11. How much did the most expensive dessert ever cost? GOOGLE AGAIN.

12. Why is 70 a weird number? **HERE**

13. Why Google Googol? **HERE**

14. How many burgers does McDonalds sell a second worldwide? **HERE**

15. If the population of the world spread across the USA , what area would we get each?

GOOGLE THE NUMBERS!

16. How many times was the most frequently married person in the world, married?

GOOGLE HIM.

17. Why is Zero Zero Zero like 123? **HERE**

18. What is the world record for the greatest number of snorts in 10 seconds? **HERE**

19. How long would it take to grow your hair to your feet? **HERE**

20. 20. What number causes the greatest loss of money in the world? **HERE**