The physical orientation of a ski or snowboard may change dramatically during a sport. These changes may include rotation in the x, y, and z axes of a full 360 degrees or more.

What does rotation look like in a graph? Consider the graph below, excerpted from a book series by Schottenbauer Publishing.

__Discussion Questions__
- How many rotations are shown on the graph?
- Identify the time segments of each of the rotations.
- What is the length of the time of each rotation?
- Describe each rotation in terms of degrees or radians of rotation in the x, y, and z axes.
- [Advanced Question] Describe each rotation in terms of angular coordinates.
- What is the angular velocity of each rotation?
- What would the graph look like if the skateboard were rotated the opposite direction around the center axis? Sketch the graphs.
- What would the graph look like if the skateboard were rotated around the other two axes? Sketch the graphs.

**Additional Information**
Schottenbauer Publishing
Fun snow skiing science experiments can be conducted in the classroom or at home! The experiment below, featuring graphs of lab equipment on artificial slopes, illustrates concepts in books from Schottenbauer Publishing.

**Snow Sport Experiment**

__Equipment__

- Block Toy(s)
- Small Toy Car(s) (Matchbox or Hot Wheels)
- Stiff Clipboards (Plastic, Cardboard, Metal)
- Cutting Board(s) (Plastic, Wood)
- Bendable Cardboard
- Protractor
- Any Book(s)
- Postal Scale

__Procedure__

Make an artificial slope with the clipboard, cutting board, and/or cardboard, by setting one end up on book(s) and the other end on a table or desk. Use a protractor to estimate the angle, if the surface is not curved. Weigh each of the toys, and compare surface area of contact with the slope. One by one, send the toys down the slope, and watch the projectile motion. Watch the block and/or toys fall off the edge of the desk, onto a mat or carpet to avoid damage to the toys or floor. Compare performance of several objects under several conditions.

__Discussion Questions__
- Describe the following in words:
- How do the trajectories (position, velocity, & acceleration) of the objects compare?
- How do wheels affect the trajectory (as opposed to a flat block surface)?
- How does mass affect the trajectory?
- How does surface area affect trajectory?

- Compare the results above with graphs and data from The Science of Snow Sports.
- Do any of the objects have similar properties?
- Do any of the surfaces have similar properties?
- Do any of the trajectories resemble a graph from the book series?

- Compare the results above with data and videos from real snow sports.
- How are real snow sport events similar?
- How are real snow sport events different?

__Additional Information__

Geometry is essential for snow sports. Take a moment to write down a few ways in which geometry affects the precision of the sport.

**Discussion Questions**
- What data is necessary to collect in order to understand the role of geometry in snow sports?
- What spatial perspectives and/or mathematical planes are important for precision?

The cover of *The Geometry of Winter Olympic Sports*, to the right above, features a cross-country skier in action.

**Discussion Questions**
- What angles can be measured on the diagram, in order to understand the accuracy of technique?
- Is any essential information missing from the picture? What is necessary in order to measure that information?

Geometry diagrams featuring snow sports are available in the following book from **Schottenbauer Publishing**:

**Geometry Workbooks**

__Additional Information__

Ski jumps are impressive aerial displays of the laws of physics. Studying jumps in the laboratory, without the presence of wind, presents data which is easier to analyze.

The following graph is excerpted from Volume 4 of The Science of Snow Sports from Schottenbauer Publishing.

__Discussion Questions__
- Using a red pen, separate the graph into the following segments: (a) At Rest on Top of Slope, (b) Trajectory on Slope, (c) Trajectory in Air, (d) Trajectory on Ground, (e) At Rest on Ground.
- Create a table with the above categories, including: (a) Initial Time, (b) Ending Time, (c) Highest x Value, (d) Lowest x Value, (e) Highest y Value, (f) Lowest y Value.
- Using the above information, calculate the average velocity during the trajectory on the slope in terms of the speed in the x direction, the y direction, and overall.
- Using the above information, calculate the average velocity in the air in terms of the speed in the x direction, the y direction, and overall.
- What occurs after the model skier hits the ground?

Additional data on snow sports can be found in the following science lab manuals from Schottenbauer Publishing:

*Graphs & Data for Science Lab: Multi-Volume Series*
- The Science of Snow Sports
- Volume 1: Force, Acceleration, & Video Analysis (Outdoor Snow & Lab)
- Volume 2: Force & Video Analysis (Plastic Models in Lab)
- Volume 3: Force & Acceleration (Ice-Topped Snow)
- Volume 4: Video Analysis (Models on Curved Surfaces in Lab)

**Anthologies of 28 Graphs**
- The Science of Winter Olympic Sports

*Graphs & Data for Science Lab: Multi-Volume Series*
- The Science of Athletic Training
- The Science of Exercise Equipment
- The Science of Gymnastics
- The Science of Yoga, Pilates, & Ballet

**Anthologies of 28 Graphs**
- The Science of Physical Fitness
- The Science of Gymnastics
- The Science of Yoga
- The Science of Dance & Ballet

__Additional Information__

A new volume of **The Science of Snow Sports** has arrived! *Volume 4* contains graphs from laboratory conditions. The volume compares motion of different objects on curved surfaces which are similar to ski slopes. The main surfaces incline a mildly-abraded piece of HDPE plastic, molded into sloping and U-shaped inclines, and a curved piece of metal sheeting molded into a ski jump. Graphs show the motion of a model skier on skis and a snowboard, plus a variety of shapes of wood blocks, a cylinder, and a rubber ball, as they travel down these slopes.

These data can be used for lesson plans by teachers and parents as supplements for traditional classes, as well as for special school projects, after-school enrichment activities, homeschool, and special science camps.

A sample graph from The Science of Snow Sports: Volume 4 is shown below:

Discussion Questions
- How far does the skier travel in the vertical plane?
- How far does the skier travel in the horizontal plane?
- Draw a sketch of the curved incline on which the skier travels.
- Describe the forces on the skier.
- Calculate the maximum velocity of the skier.
- What event occurs towards the end of the trajectory? Why?
- Describe the entire motion of the skier, using a full paragraph.
- The mass of the skier is 35.93 g and the mass of the skis are 4.60 g. The dimensions of the skis in cm are 7.1 x 1.3 x 0.2. What additional calculations can be made with these values?

Additional graphs similar to those above can be found in the following science lab manuals from Schottenbauer Publishing:

*Graphs & Data for Science Lab: Multi-Volume Series*
- The Science of Snow Sports
- Volume 1: Force, Acceleration, & Video Analysis (Outdoor Snow & Lab)
- Volume 2: Force & Video Analysis (Plastic Models in Lab)
- Volume 3: Force & Acceleration (Ice-Topped Snow)
- Volume 4: Video Analysis (Models on Curved Surfaces in Lab)

**Anthologies of 28 Graphs**
- The Science of Winter Olympic Sports

__Additional Information__