Lessons on Friction & Collisions

Friction and collisions are concepts relevant to both ice hockey and figure skating. Consider the graph below, excerpted from a book by Schottenbauer Publishing:

Discussion Questions

1. How is air hockey similar to ice hockey? How is it different?
2. How is air hockey similar to ice skating? How is it different?
3. What happens when a hockey puck collides with a stick? 
4. How are the phenomena in this graph similar to collisions between an ice hockey puck and stick? How are they different?
5. What is the role of friction in ice skating? What does friction do to the motion of a hockey puck or a skater? 
6. How does this graph demonstrate friction?
7. How are the phenomena in this graph similar to friction experienced by an ice hockey puck? How are they different?
8. How are the phenomena in this graph similar to friction experienced by an ice skater? How are they different?

Additional sample graphs are available in a free pamphlet from the publisher's webpage.

Additional Information

Schottenbauer Publishing

Free Education Resources

Comparing Ice Skating Equipment in the Lab

What types of measurements are ideal for understanding ice skating? Take a moment to write down a list of at least four types of data to collect and compare. What types of equipment are necessary to measure each type? What physics concepts are relevant?

Many types of interesting data are available for comparison in the book The Science of Ice Skating: Volume 1 (Extended Edition) from Schottenbauer Publishing. Data include position, velocity, acceleration, and force for the following equipment:

• Surface Types
• Ice
• Synthetic Ice
• Wet
• Dry
• Skate Types
• Bob Skates
• Child Double-Runner Skates
• Hockey Skates
• Youth
• Adult
• Figure Skates
• 2 Sizes
• 2 Types of Blades
• Blade Preparation
• Sharpened
• Unsharpened
• Skate Mass
• None
• Added 2.5 pounds of weight

Additional types of data include:

• Hockey Puck Motion
• Vertical Motions (Force)
• Stepping
• Jumping
• Skate Support for Ankles (Force)
• Ice Melting (Temperature)

Free sample graphs are available in a free pamphlet from the publisher's webpage.

Additional Information

Schottenbauer Publishing

Free Education Resources

Video Analysis of "Cool Skating Move"

As with any sport, ice skating can be analysed in graphs. Consider the following graph below, excerpted from the upcoming Volume 9 of Glide, Spin, & Jump! The Science of Ice Skating by Schottenbauer Publishing. 

Discussion Questions

1. What body parts are moving in this example?
2. Which body part moves the most in the x direction? In the y direction?
3. What is the name of this move?

Now, consider the following pictures, excerpted from the video. (This move is shown in the YouTube Video Cool Skating Move.) 

Discussion Questions

1. Is this move in the first or second half of the graph?
2. What is the primary motion which occurs between these two pictures?
3. What concept(s) from physics are relevant for this move?
4. Is this move found in (a) figure skating, (b) ice hockey, or (c) both?

The diagram below highlights the move on the graph.

Discussion Questions

1. Which body part moves the most during this segment of the graph?
2. Which body part moves the most in the x direction? In the y direction?

Additional free graphs are available in a free pamphlet from the publisher's webpage. 

The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of ice skating, figure skating, and hockey:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Ice Skating 
• Volume 1: Translational Motion
• Volume 2: Rotational Motion (Curves)
• Volume 3: Rotational Motion (Spins)
• Volume 4: Jumps
• Volume 5: Ice Hockey
• Volume 6: Biophysics
• Volume 7: Video Analysis
• Volume 8: Reference Manual
• The Science of Hockey
• Volume 1: Force, Acceleration, & Video Analysis of Pucks & Balls
• Volume 2: Force & Acceleration of Sticks, plus Biophysics
• Volume 3: Video Analysis of Ice, Field, & Street Hockey Sticks

Anthologies of 28 Graphs

• The Science of Figure Skating
• The Science of Ice Hockey
• The Science of Winter Olympic Sports

Additional Information

Schottenbauer Publishing

Free Education Resources

The Science of Jumping

What happens when an ice skater jumps? The answer can be modeled in various levels of difficulty. One the simplest level, assume that the skater is simply a point mass object, without movement within the body. In this analysis, acceleration occurs in three planes, leading to changes in altitude and rotation. 

On the most complex level, the skater's body must be analysed as separate components moving in relation to the center of mass, which for most humans is approximately in the center of the abdomen or hips.

Discussion Questions

1. What everyday motions are related to skating? 
2. If skater motion were to be studied by making comparisons between graphs, which types of motions should be compared?

Volume 4 of Glide, Spin, & Jump: The Science of Ice Skating contains graphs of acceleration, force, and vertical distance in a series of motions completed by the author. 

Graphs of Motion

• Standing to Squatting Position
• Jumping with No Rotation
• Rotation with No Jumping
• Skating Jumps on Land
• Skating Jump on Synthetic Ice

Jumps on Land

• Half Jumps
• Stag
• Waltz
• Ballet 
• Mazurka
• Half Axel
• Single & Double Jumps
• Salchow
• Loop
• Toe Loop
• Flip
• Lutz
• Axel

The following two graphs are excerpted from Volume 4 of Glide, Spin, & Jump: The Science of Ice Skating. Notice that these jumps, completed in a purely vertical direction on land, are simpler to analyze, because they lack the horizontal translational motion across the ice. 

Discussion Questions

1. What are the major differences between these graphs?
2. In these graphs, how can direction be determined? What direction is up?
3. In each graph, what occurs in the vertical direction? 
4. In the lower graph, what is the pattern of acceleration in the horizontal plane during the rotations?
5. In each graph, what sort of tilt (side to side) occurs?
6. Is it better to locate the wireless device on the stomach or chest? Why?
7. Describe the role of knee motions during each of the above jumps, and their effects on acceleration.
8. What is the role of non-relevant movements (such as the motion of breathing) in these graphs, if any?
9. What is the role of error or random motion in these graphs, if any? 
10. Are these clean (technically correct) jumps? If not, what would the acceleration pattern be during a clean jump?
11. What would a fall look like in a graph of acceleration?
12. What would the graphs look like if the jumps were completed on the ice?

Additional free graphs of ice skating are available in a free pamphlet from the publisher's webpage. A humorous cartoon animation of an ice skater, showing approximate force vectors, is available from the publisher's YouTube channel.

The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of ice skating, figure skating, and hockey:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Ice Skating 
• Volume 1: Translational Motion
• Volume 2: Rotational Motion (Curves)
• Volume 3: Rotational Motion (Spins)
• Volume 4: Jumps
• Volume 5: Ice Hockey
• Volume 6: Biophysics
• Volume 7: Video Analysis
• Volume 8: Reference Manual
• The Science of Hockey
• Volume 1: Force, Acceleration, & Video Analysis of Pucks & Balls
• Volume 2: Force & Acceleration of Sticks, plus Biophysics
• Volume 3: Video Analysis of Ice, Field, & Street Hockey Sticks

Anthologies of 28 Graphs

• The Science of Figure Skating
• The Science of Ice Hockey
• The Science of Winter Olympic Sports

In addition, the following books are suitable for younger children learning geometry:

Geometry Workbooks

• The Geometry of Figure Skating
• The Geometry of Winter Olympic Sports 

Additional Information

Schottenbauer Publishing

Free Education Resources

How Does Geometry Affect Ice Skating?

On the surface level, both the technique and beauty of ice skating can be described by geometry, in terms of the angles of knee bends and arm positions. On a technical level, geometry is essential for understanding the science of ice skating, including the physics of force and motion.

The books The Geometry of Winter Olympic Sports and The Geometry of Figure Skating contain diagrams which introduce children and teens to the task of identifying angles in ice skating. Consider the diagram below, excerpted from page 25 of The Geometry of Winter Olympic Sports (Copyright 2014, All Rights Reserved).

Discussion Questions

1. How many angles are formed in this diagram?
2. From a casual analysis, what types of angles (Acute/Obtuse/Right) are located in the diagram? Indicate the location of each angle.
3. In order to analyze the angles in this diagram, where should the coordinate axis be placed? Why? Is it necessary to identify more than one coordinate axis? Why or why not? If so, where should the axes be placed?
4. Using a protractor, measure all the angles in the diagram that are relevant to the art or physics of skating.
5. Is it possible to identify the direction of motion from this diagram? Why or why not?
6. Is this a figure skater or a hockey player? Justify your answer.

Assistance answering some of these questions may be found by watching the video How to Use Geometry Workbooks on the publisher's YouTube channel.

The following books from Schottenbauer Publishing contain geometry diagrams relevant to ice skating, figure skating, and hockey. 

Geometry Workbooks

• The Geometry of Figure Skating
• The Geometry of Winter Olympic Sports 

Additional Information

Schottenbauer Publishing

Free Education Resources

Skater in Motion: x-y Plots of Movement

In elementary school, math students learn the graph-reading skills. How often do these same students enjoy applying math to real-life data? In books from Schottenbauer Publishing, students have the opportunity to decode graphs showing movement during popular sports.

The graph below (Copyright 2014, All Rights Reserved), excerpted from the book series Glide, Spin, & Jump: The Science of Ice Skating from Schottenbauer Publishing, shows an ice skater in forward motion.

Discussion Questions

1. What is the range of each variable in each graph? Include x, y, and t as variables in your analysis.
2. In this sample, which leg is used for pushing off? Which leg moves forward first? 
3. Use the information from the graph to draw the body in physical space, at a minimum of 4 time points.
4. Is the right knee ever in front of the right hip? Is the right ankle ever in front of the right knee or right hip? Describe the sequence of motion.
5. Is the left knee ever in front of the left hip? Is the left ankle ever in front of the left knee or left hip? Describe the sequence of motion.

Additional free graphs are available in a free pamphlet from the publisher's webpage. 

The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of ice skating, figure skating, and hockey:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Ice Skating 
• Volume 1: Translational Motion
• Volume 2: Rotational Motion (Curves)
• Volume 3: Rotational Motion (Spins)
• Volume 4: Jumps
• Volume 5: Ice Hockey
• Volume 6: Biophysics
• Volume 7: Video Analysis
• Volume 8: Reference Manual
• The Science of Hockey
• Volume 1: Force, Acceleration, & Video Analysis of Pucks & Balls
• Volume 2: Force & Acceleration of Sticks, plus Biophysics
• Volume 3: Video Analysis of Ice, Field, & Street Hockey Sticks

Anthologies of 28 Graphs

• The Science of Figure Skating
• The Science of Ice Hockey
• The Science of Winter Olympic Sports

In addition, the following books are suitable for younger children learning geometry:

Geometry Workbooks

• The Geometry of Figure Skating
• The Geometry of Winter Olympic Sports 

Additional Information

Schottenbauer Publishing

Free Education Resources

Spinning on Ice

Physics divides motion into two general types: translational (straight) motion and rotational (curved) motion. Whether it is a figure skater, hockey skater, or puck rotating on the ice, the same laws of physics apply. 

The graph below (Copyright 2014, All Rights Reserved), excerpted from the book series Glide, Spin, & Jump: The Science of Ice Skating from Schottenbauer Publishing, shows a rod rotating around a central axis.

Discussion Questions

1. Describe the four variables contained in the graph. What is the range of each variable?
2. How is position measured in the graph? What is the unit of measurement?
3. How many times is force applied to the rod? 
4. When force is applied, what happens to the rod?
5. Why does the rod slow down, and motion stop?
6. What is the definition of acceleration? 
7. Why does acceleration change so much, when the velocity and position do not?

Additional free graphs are available in a free pamphlet from the publisher's webpage. 

The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of ice skating, figure skating, and hockey:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Ice Skating 
• Volume 1: Translational Motion
• Volume 2: Rotational Motion (Curves)
• Volume 3: Rotational Motion (Spins)
• Volume 4: Jumps
• Volume 5: Ice Hockey
• Volume 6: Biophysics
• Volume 7: Video Analysis
• Volume 8: Reference Manual
• The Science of Hockey
• Volume 1: Force, Acceleration, & Video Analysis of Pucks & Balls
• Volume 2: Force & Acceleration of Sticks, plus Biophysics
• Volume 3: Video Analysis of Ice, Field, & Street Hockey Sticks

Anthologies of 28 Graphs

• The Science of Figure Skating
• The Science of Ice Hockey
• The Science of Winter Olympic Sports

Additional Information

Schottenbauer Publishing

Free Education Resources

Real Ice Skating Data from Child Double Runner Skates!

Easy access to the science of ice skating is provided by several book series from Schottenbauer Publishing! Books contain graphs, data, and diagrams of ice skating, figure skating, and hockey.

The graphs below are excerpted from Volume 1 of Glide, Spin, & Jump: The Science of Ice Skating, as well as a free pamphlet from the publisher. These graphs show a child's double-runner skate being pulled along a piece of real ice with a force meter, while position, velocity, and acceleration are measured by a motion detector from the back.

Discussion Questions

1. For each graph, describe the motion of the skate in words. 
2. How far does the skate travel in each graph?
3. What is the maximum force on the skate?
4. Is the force on the skate similar to the forces incurred during real skating?
5. From these two graphs, can you determine the mass of the skate?
6. How much physical work is occurs during the movement of the skate? 
7. In which graph is the friction greater?
8. Can the friction be calculated from these graphs?
9. How accurate are these graphs? What is the margin of error, if any?
10. Are these graphs relevant for real skaters? If so, how? 

Additional free graphs are available in a free pamphlet from the publisher's webpage. 

The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of ice skating, figure skating, and hockey:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Ice Skating, Vol. 1-8
• The Science of Hockey, Vol. 1-3

Anthologies of 28 Graphs

• The Science of Figure Skating
• The Science of Ice Hockey
• The Science of Winter Olympic Sports

In addition, the following books are suitable for younger children learning geometry:

Geometry Workbooks

• The Geometry of Figure Skating
• The Geometry of Winter Olympic Sports 

Additional Information

Schottenbauer Publishing

Free Education Resources

Cool Figure Skating Move: Before and After Photos!

A new YouTube Video shows a cool figure skating move on synthetic ice. Here are the before and after photos! 

Let's think about the physics of this move. What happens in order for the skater to turn from one position to the other? How does the rotation begin? What stops the rotation? Watch the video on YouTube for more details!

Additional information on the science of ice skating is available on the Schottenbauer Publishing website. Books include the following:

Geometry Series

• The Geometry of Winter Olympic Sports
• The Geometry of Figure Skating

Graphs & Data for Science Lab (Book Series)

• The Science of Ice Skating
• The Science of Hockey

Anthologies of 28 Graphs

• The Science of Winter Olympic Sports
• The Science of Figure Skating
• The Science of Ice Hockey

Additional Information

Schottenbauer Publishing

Free Education Resources

Ice Skate Comparison

Ice skates are not all the same! Two extremes are hockey and figure skates. Because hockey skates have a smooth, curved blade on the front and the back, they can feasibly be tilted almost to a right angle while still gliding across the ice! In comparison, the blade of a figure skate has grooved teeth on the front, and a flat back blade. These features prohibit tilting of the figure skates during gliding. 

What are the angles of maximum tilt for each of these skates?

Hockey Skate (Left) and Figure Skate (Right)

Two additional types of skates are shown below: bob skates and child double-runner skates. These skates are for children and are not traditionally sharpened, so they do not glide over the ice. How far could these skates rotate upwards to the front or back, before hitting the plastic or tipping over?  

Bob Skate

 Child Double-Runner Skate

Additional information on the science of ice skating is available on the Schottenbauer Publishing website. Books include the following:

Geometry Series

• The Geometry of Winter Olympic Sports
• The Geometry of Figure Skating

Graphs & Data for Science Lab (Book Series)

• The Science of Ice Skating
• The Science of Hockey

Anthologies of 28 Graphs

• The Science of Winter Olympic Sports
• The Science of Figure Skating
• The Science of Ice Hockey

Additional Information

Schottenbauer Publishing

Free Education Resources

Learning to Glide, Spin, and Jump!

The science and math of ice skating are topics of new books from Schottenbauer Publishing. Presenting data from real figure skating and hockey collected by the science writer and publisher M. Schottenbauer, Ph.D., these books bring the "high tech" end of skating to audiences everywhere!

In these books, students can enjoy learning about common moves from figure skating and hockey. One series of books, written for elementary school students, focuses on geometry. Two series of science books feature graphs and data; these illustrate common mathematical functions, plus a variety of concepts from physics and biophysics. The science books can be integrated into classes such as math, physical science, physics, physical education, and health, anywhere from 7th grade through high school, as well as some introductory college and university classes. 

The books directly pertaining to ice skating and hockey include the following:

Geometry Workbooks

• The Geometry of Figure Skating
• The Geometry of Winter Olympic Sports

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Ice Skating 
• Volume 1: Translational Motion
• Volume 2: Rotational Motion (Curves)
• Volume 3: Rotational Motion (Spins)
• Volume 4: Jumps
• Volume 5: Ice Hockey
• Volume 6: Biophysics
• Volume 7: Video Analysis
• Volume 8: Reference Manual
• The Science of Hockey
• Volume 1: Force, Acceleration, & Video Analysis of Pucks & Balls
• Volume 2: Force & Acceleration of Sticks, plus Biophysics
• Volume 3: Video Analysis of Ice, Field, & Street Hockey Sticks

Anthologies of 28 Graphs

• The Science of Figure Skating
• The Science of Ice Hockey
• The Science of Winter Olympic Sports 

These books are complemented by a series of science books on other popular sports topics, including Olympic sports, athletic training, exercise equipment, gymnastics, yoga, ballet, and more. Topics related to ice skating include:

Geometry Workbooks

• The Geometry of Yoga
• The Geometry of Ballet
• The Geometry of Gymnastics

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Athletic Training
• Volume 1: Force & Acceleration
• Volume 2: Biophysics
• Volume 3: Video Analysis 
• The Science of Exercise Equipment 
• Volume 1: Force & Acceleration
• Volume 2: Biophysics
• Volume 3: Video Analysis
• The Science of Yoga, Pilates, & Ballet 
• Volume 1: Force & Acceleration
• Volume 2: Biophysics
• Volume 3: Video Analysis
• The Science of Gymnastics 
• Volume 1: Force & Acceleration
• Volume 2: Biophysics
• Volume 3: Video Analysis

Anthologies of 28 Graphs

• The Science of Physical Fitness
• The Science of Dance & Ballet
• The Science of Gymnastics
• The Science of Yoga

Most of the books above are available in both English and German translation. The books pertaining to the geometry of Olympic sports are also available in 15 world languages. 

The same publisher offers similar books on additional popular topics, including sports, transportation, construction, environment, music, entertainment, and general physics. All of these book series are available in several formats and languages, including the following:

Geometry Workbooks

• Print & E-Book Editions
• Available in English & German
• Olympics Books Available in 15 Languages

Graphs & Data for Science Lab: Multi-Volume Series

• Print Editions
• Available in English & German

Anthologies of 28 Graphs

• Print Editions
• English Only

Additional Information

Schottenbauer Publishing

Free Education Resources

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With Kindle Unlimited ($9.99/month) at Amazon.com, you can read all e-books from Schottenbauer Publishing for no extra charge! Amazon offers Free 30 Day Trials of Kindle Unlimited. With this deal, trial members can read all Schottenbauer Publishing e-books free! This includes all the geometry workbooks, plus "The World in a Graph," "Alphabets of the World," textbooks on the science of music, all the e-book puzzles, and the educational novels by M. Schottenbauer, Ph.D.